# Recent questions tagged geometry

1 vote
1
In a triangle $\text{ABC}, \angle \text{BCA} = 50^{\circ}. \text{D}$ and $\text{E}$ are points on $\text{AB}$ and $\text{AC},$ respectively, such that $\text{AD = DE}.$ If $\text{F}$ is a point on $\text{BC}$ such that $\text{BD = DF},$ then $\angle \text{FDE, in degrees},$ is equal to $96$ $72$ $80$ $100$
1 vote
2
Let $\text{ABCD}$ be a parallelogram. The lengths of the side $\text{AD}$ and the diagonal $\text{AC}$ are $10 \; \text{cm}$ and $20 \; \text{cm},$ respectively. If the angle $\angle \text{ADC}$ is equal to $30^{\circ}$ then the area of the parallelogram, in sq. cm, is $\frac{25(\sqrt{5} + \sqrt{15})}{2}$ $25 (\sqrt{5} + \sqrt{15})$ $\frac{25 (\sqrt{3} + \sqrt{15})}{2}$ $25 (\sqrt{3} + \sqrt{15})$
1 vote
3
The cost of fencing a rectangular plot is $₹ \; 200 \; \text{per ft}$ along one side, and $₹ \; 100 \; \text{per ft}$ along the three other sides. If the area of the rectangular plot is $60000 \; \text{sq. ft},$ then the lowest possible cost of fencing all four sides, in $\text{INR},$ is $160000$ $100000$ $120000$ $90000$
1 vote
4
A park is shaped like a rhombus and has area $96 \; \text{sq m}.$ If $40 \; \text{m}$ of fencing is needed to enclose the park, the cost, in $\text{INR},$ of laying electric wires along its two diagonals, at the rate of $₹ \; 125 \; \text{per m},$ is
1 vote
5
If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is $\sqrt{13} + \sqrt{12}$ $\sqrt{37} + \sqrt{13}$ $\frac{\sqrt{37} + \sqrt{13}}{2}$ $\frac{\sqrt{13} + \sqrt{12}}{2}$
1 vote
6
The sides $\text{AB}$ and $\text{CD}$ of a trapezium $\text{ABCD}$ are parallel, with $\text{AB}$ being the smaller side. $\text{P}$ is the midpoint of $\text{CD}$ and $\text{ABPD}$ is a parallelogram. If the difference between the areas of the parallelogram $\text{ABPD}$ and the ... $\text{in sq cm},$ of the trapezium $\text{ABCD}$ is $25$ $30$ $40$ $20$
1 vote
7
Let $\text{D}$ and $\text{E}$ be points on sides $\text{AB}$ and $\text{AC},$ respectively, of a triangle $\text{ABC},$ such that $\text{AD}$ : $\text{BD} = 2 : 1$ and $\text{AE}$ : $\text{CE} = 2 : 3.$ If the area of the triangle $\text{ADE}$ is $8 \; \text{sq cm},$ then the area of the triangle $\text{ABC, in sq cm},$ is
1 vote
8
If the area of a regular hexagon is equal to the area of an equilateral triangle of side $12 \; \text{cm},$ then the length, in cm, of each side of the hexagon is $6 \sqrt{6}$ $2 \sqrt{6}$ $4 \sqrt{6}$ $\sqrt{6}$
1 vote
9
Suppose the length of each side of a regular hexagon $\text{ABCDEF}$ is $2 \; \text{cm}.$ It $\text{T}$ is the mid point of $\text{CD},$ then the length of $\text{AT, in cm},$ is $\sqrt{15}$ $\sqrt{13}$ $\sqrt{12}$ $\sqrt{14}$
1 vote
10
A circle of diameter $8 \; \text{inches}$ is inscribed in a triangle $\text{ABC}$ where $\angle \text{ABC} = 90^{\circ}.$ If $\text{BC} = 10 \; \text{inches}$ then the area of the triangle in $\text{square inches}$ is
11
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$ $\frac{12 \pi}{5}$ $\frac{123 \pi}{7}$ $\frac{205 \pi}{9}$
12
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$ $14$ $13$ $15$
13
In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5 \; \text{cm}, \; \text{BC} = 4 \; \text{cm},$ the area of the trapezium in $\text{sq. cm}$ is
14
The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area, $\text{R},$ of the rectangle, both in $\text{sq cm},$ ... the sides of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is $24$ $27$ $21$ $18$
15
Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and $\text{B}$ where $\text{A}$ is located $4 \; \text{meters}$ north of $\text{O}$ and $\text{B}$ is located $3 \; \text{meters}$ east of $\text{O}.$ Then, the length of $\text{PQ}$, in meters, is nearest to $7.2$ $7.8$ $6.6$ $8.8$
16
Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$ has length $6 \; \text{cm}$ and is a tangent to $\text{C}2,$ then the diameter, in $\text{cm},$ of $\text{C}1$ is
1 vote
17
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s.$ Then the area of the triangle is $\frac{\sqrt{3}s^{2}}{2}$ $\frac{s^{2}}{\sqrt{3}}$ $\frac{2s^{2}}{\sqrt{3}}$ $\frac{s^{2}}{2 \sqrt{3}}$
1 vote
18
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two$-$thirds of the painted area then the perimeter of the rectangle in inches is $5\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$ ... $3\sqrt{\pi }\left ( 5+\frac{12}{\pi} \right )$ $4\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$
1 vote
19
A circle is inscribed in a thombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\frac{3\pi }{25}$ $\frac{2\pi }{15}$
20
A circular garden twenty feet in diameter is surrounded by a path three feet wide. What is the area of the path? $51 \pi$ square feet $60 \pi$ square feet $69 \pi$ square feet $90 \pi$ square feet
21
What is the area of a semicircle with a diameter of $16$ inches? $32 \pi$ square inches $64 \pi$ square inches $128 \pi$ square inches $256 \pi$ square inches
Which of the following figures has the largest perimeter $(1 \text{ foot} = 12 \text{ inches})$ a square with a diagonal of $5$ feet a rectangle with sides of $3$ feet and $4$ feet an equilateral triangle with a side equal to $48$ inches a regular hexagon whose longest diagonal is $6$ feet
The perimeter of a parallelogram is $50$ cm. The length of the parallelogram is $5$ cm more than the width. Find the length of the parallelogram. $15$ cm $11$ cm $5$ cm $10$ cm
A conical tent is to accommodate $10$ persons. Each person must have $6$ $m$^{2}$space to sit and$30\;m^{3}$of air to breath. What will be height of cone ?$37.5m150m75m15m$0 votes 4 answers 25 In a swimming-pool$90$m by$40$m,$150$men take a dip. If the average displacement of water by a man is$8$cubic metres, what will be rise in water level ?$30$cm$33.33$cm$20.33$cm$25$cm 0 votes 1 answer 26 If$A$be the area of a right angled triangle and$b$be one of the sides containing the right angle, then the length of altitude on the hypotenuse is :$\frac{2Ab}{\sqrt{4b^{4}+A^{2}}}\frac{Ab}{\sqrt{b^{4}+4A^{2}}}\frac{2Ab}{\sqrt{b^{4}+4A^{2}}}\frac{Ab}{\sqrt{4b^{4}+A^{2}}}$2 votes 1 answer 27 In an acute angled triangle$ABC$, if$\tan \left(A+B-C \right)=1$and$\sec \left(B+C-A \right)=2$, Find angle$A$.$60^\circ45^\circ30^\circ90^\circ$0 votes 1 answer 28 What will be area of the rhombus with equations of sides$ax \pmby \pm c$=$1$?$\frac{3c^{2}}{ab}$sq. units$\frac{4c^{2}}{ab}$sq. units$\frac{2c^{2}}{ab}$sq. units$\frac{c^{2}}{ab}$sq. units 0 votes 1 answer 29 If$\left (-4, 0 \right), \left(1, -1 \right)$are two vertices of a triangle whose area is$4$Sq units then its third vertex lies on :$y=x5x+y+12=0x+5y-4=0x-5y+4=0$1 vote 1 answer 30 In a triangle$XYZ$,$P$and$Q$are points on${XY,XZ}$respectively such that$XP=2PY$,$XQ=2QZ$, then the ratio, of area of$\triangle XPQ$and area of$\triangle XYZ$is:$4:92:33:29:4$0 votes 1 answer 31 A conical tent is to accommodate$10$persons. Each person must have$6m^{2}$space to sit and$30m^{3}$of air to breath. What will be height of cone?$37.5$m$150$m$75$m$15$m 0 votes 1 answer 32 In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with$38$bangles. If he wanted to increase the size of square by one bangle each side of the square he found that$25$bangles fall short of in completing the square. The actual number of bangles which he had with him the shop was_________.$16909995381000$0 votes 0 answers 33$A,B,C$are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can walk,ride,drive a km in$a,b,c$minutes respectively. If he starts from$B$, he takes$a-b+c$... from$A$he takes$c+b-a$hrs. The length of the triangle is: (assume the motion in anticlockwise direction)$60a50a40a65a$0 votes 1 answer 34 A cylindrical box of radius$5$cm contains$10$solid spherical balls each of radius$5$cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is:$\dfrac{2500\pi}{3}$cubic cm$500\pi$cubic cm$2500\pi$cubic cm$\dfrac{5000\pi}{3}$cubic cm 0 votes 1 answer 35 If$(-4,0),(1,-1)$are two vertices of a triangle whose area is$4$Sq units then its third vertex lies on:$y=x5x+y+12=0x+5y-4=0x-5y+4=0$0 votes 1 answer 36 For a sphere of radius$10$cm, the numerical value of the surface area is how many percent of the numerical value of its volume?$26.5\%24\%30\%45\%$0 votes 1 answer 37 Line$AB$is$24$metres in length and is tangent to the inner one of the two concentric circles at point$C.$Points$A$and$B$lie on the circumference of the outer circle. It is known that the radii of the two circles are integers. The radius of the outer circle is$13$m$5$m$7$m$4$m 0 votes 1 answer 38 A rectangular field is to be fenced on three sides leaving a side of$20$feet uncovered. If the area of the field is$680$sq feet, how many feet of fencing will be required?$34406888$0 votes 2 answers 39 If$10$,$12$and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible ?$712913$0 votes 1 answer 40 The length of a rope, to which a cow is tied, is increased from$19$m to$30$m. How much additional ground will it be able to graze ? Assume that the cow is able to move on all sides with equal ease. Use$\pi = \frac{22}{7}$in your calculations.$1696$sq m$1694$sq m$1594$sq m$1756\$ sq m