A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 7 , 2 , and 9 , respectively. What is the rectangle's area?

1 Answer
Mar 25, 2016

≈ 60.374 square units

Explanation:

The area of the rectangle = 9B , where B has to be found.

Since the triangle is right , with A the hypotenuse , we can find B using color(blue)" Pythagoras' theorem "

then : A^2 = B^2 + C^2 rArr B^2 = A^2 - C^2

B^2 = 7^2 - 2^2 = 49 - 4 = 45

now B^2 = 45 rArr B = sqrt45

and area of rectangle = 9B = 9xxsqrt45 ≈ 60.374