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 10 , 8 , and 4 , respectively. What is the rectangle's area?

1 Answer
Jim G.
Apr 8, 2016

24 square units

Explanation:

The area of the rectangle = color(blue)" 4B"

To calculate the value of the area , require to find B.

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

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

rArr B^2 = 10^2 - 8^2 = 100 - 64 = 36

now B^2 = 36 rArr B = sqrt36 = 6

and area of rectangle = 4B = 4xx6 = 24" square units "

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