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1 vote

Let $\text{ABC}$ be a right-angled triangle with $\text{BC}$ as the hypotenuse. Lengths of $\text{AB}$ and $\text{AC}$ are $15$ km and $20$ km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from $\text{A}$ at a speed of $30$ km per hour is

- $23$
- $22$
- None of these
- $24$

1 vote

Given that, $ABC$ be a right-angled triangle with $BC$ as the hypotenuse.

Also, $AB=15$ km and $AC=20$ km.

We can draw the diagram.

By using the Pythagorean theorem,

$(BC)^{2} = (AB)^{2} + (AC)^{2}$

$\Rightarrow$ $ (BC)^{2} = (15)^{2} + (20)^{2}$

$\Rightarrow$ $ (BC)^{2} = 225 + 400 $

$\Rightarrow$ $ (BC)^{2} = 625 $

$\Rightarrow$ $ (BC)^{2} = (25)^{2} $

$\Rightarrow$ $ \boxed{BC = 25\;\text{km}} $

The area of the $\triangle ABC,$ we can write in two ways.

$\frac{1}{2}\times AB\times AC = \frac{1}{2}\times BC\times AD$

$\Rightarrow 15\times 20 = 25 \times AD $

$\Rightarrow \boxed{AD = 12\;\text{km}}$

$\therefore$ The required time $= \dfrac{12\;\text{km}}{30 \;\frac{\text{km}}{\text{hour}}} = \dfrac{12 }{30 }\times 60$ minute $= 24$ minutes.

Correct Answer $ : \text{D}$