# Recent questions tagged geometry

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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 $\text{AD = DE}.$ I...
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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 a...
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The cost of fencing a rectangular plot is $\text{₹} \; 200 \; \text{per ft}$ along one side, and $\text{₹} \; 100 \; \text{per ft}$ along the three other sides. If ...
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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 elect...
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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}$$\sqrt{37} +... 1 answer 6 The sides \text{AB} and \text{CD} of a trapezium \text{ABCD} are parallel, with \text{AB} being the smaller side. \text{P} is the midpoint of \text{CD} and \... 1 answer 7 Let \text{D} and \text{E} be points on sides \text{AB} and \text{AC}, respectively, of a triangle \text{ABC}, such that \text{AD} : \text{BD} = 2 : 1 and ... 1 answer 8 If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 \; \text{cm}, then the length, in cm, of each side of the hexagon is 6 \sqr... 1 answer 9 Suppose the length of each side of a regular hexagon \text{ABCDEF} is 2 \; \text{cm}. It \text{T} is the mid point of \text{CD}, then the length of \text{AT, in ... 1 answer 10 A circle of diameter 8 \; \text{inches} is inscribed in a triangle \text{ABC} where \angle \text{ABC} = 90^{\circ}. If \text{BC} = 10 \; \text{inches} then the ar... 0 answers 11 The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is \frac{14 \pi}{3}$$\frac{12 \pi}{5}$$\frac{123 \pi... 0 answers 12 The points (2,1) and ( – 3, – 4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then \text{c} is 12$$14$...
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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... 1 answer 14 ​​​​​​​​​​​​​​​​​​​​​​​​​​​​The sum of the perimeters of an equilateral triangle and a rectangle is$90 \; \text{c...
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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 ...
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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 $\text{C}1$...
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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 o...
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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-thir...
A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\f... 1 answer 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 fe... 1 answer 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 1 answer 22 Which of the following figures has the largest perimeter$(1 \text{ foot} = 12 \text{ inches})$a square with a diagonal of$5$feeta rectangle with sides of$3$feet and ... 1 answer 23 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$10$... 2 answers 24 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 ?$37.5\;m$$150\... 4 answers 25 In a swimming-pool 90 m by 40 m, 150 men take a dip. If the average displacement of water by a man is 8 cubic metres, what will be rise in water level ?30 cm33... 1 answer 26 If A be the area of a right angled triangle and b be one of the sides containing the right angle, then the length of altitude on the hypotenuse is :\frac{2Ab}{\sqrt{... 1 answer 27 In an acute angled triangle ABC, if \tan \left(A+B-C \right)=1 and \sec \left(B+C-A \right)=2, Find angle A.60^\circ$$45^\circ$$30^\circ$$90^\circ$1 answer 28 What will be area of the rhombus with equations of sides$ax \pmby \pm c$=$1$?$\frac{3c^{2}}{ab}$sq. units$\frac{4c^{2}}{ab}$sq. units$\frac{2c^{2}}{ab}$sq. units$\...
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=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=... 1 answer 30 In a triangle XYZ, P and Q are points on {XY,XZ} respectively such that XP=2PY, XQ=2QZ, then the ratio, of area of \triangle XPQ and area of \triangle XYZ... 1 answer 31 A conical tent is to accommodate 10 persons. Each person must have 6m^{2} space to sit and 30m^{3} of air to breath. What will be height of cone?37.5 m150 m75... 1 answer 32 In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles. If he wanted to increase the size of square by one ban... 0 answers 33 A,B,C are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can ... 1 answer 34 A cylindrical box of radius 5 cm contains 10 solid spherical balls each of radius 5 cm. If the topmost ball touches the upper cover of the box, then the volume of t... 2 answers 35 If (-4,0),(1,-1) are two vertices of a triangle whose area is 4 Sq units then its third vertex lies on:y=x$$5x+y+12=0$$x+5y-4=0$$x-5y+4=0$
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\%$$45\% 1 answer 37 Line AB is 24 metres in length and is tangent to the inner one of the two concentric circles at point C. Points A and B lie on the circumference of the outer ci... 1 answer 38 A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq feet, how many feet of fencing will be requ... 2 answers 39 If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible?7$$12$$9$$13$
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 mov...