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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

1. $23$
2. $22$
3. None of these
4. $24$

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 $: \text{D}$

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