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

Question

Accepted Answer

24 — Easy The shortest path from $A$ to the hypotenuse is the perpendicular (altitude) from $A$. Compute it via "area two ways", then convert the distance to time at $30$ km/h. A B C 15 20 12 &#9654; Replay 1 Hypotenuse. Legs $AB=15,\ AC=20$, right angle at $A$: $$\begin{aligned} &BC=\sqrt{15^2+20^2}=\sqrt{625}=25 \end{aligned}$$ 2 Altitude from $A$ to $BC$. Area via the two legs equals area via the hypotenuse and altitude $d$: $$\begin{aligned} &	frac12\cdot 15\cdot 20=	frac12\cdot 25\cdot d\ &\R

CAT 2017 Slot 1 — QA Question 20

Answer & solution

Related Basics of Triangles questions