Bunuel wrote:

Isosceles right triangle ABC has an area of 72. What is its perimeter?

A. 12+6√2

B. 16+8√2

C. 18+9√2

D. 20+10√2

E. 24+12√2

As all we're given is the area, we'll work with area-related equations.

This is a Precise approach.

Since ABC is a right triangle then its area is the product of its legs times two.

Since it is isosceles, its legs are equal to each other.

So, if x is the lenght of a leg than x^2/2 = 72 --> x^2 = 144 --> x = 12.

Then the hypotenuse is 12√2 (as this is a 90-45-45 triangle) so the perimeter is 24+12√2

(E) is our answer.

_________________

David

Senior tutor at examPAL

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