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 , 4 , and 12 , respectively. What is the rectangle's area?

1 Answer
Jim G.
May 7, 2016

≈ 68.93 square units

Explanation:

Here is a sketch (not to scale)

enter image source here

The area of the rectangle = 12B

To calculate the area we require to know the value of B.

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

The hypotenuse is A hence A^2=B^2+C^2

and rearranging we get

B^2=A^2-C^2=7^2-4^2=33

now B^2=33rArrB=sqrt33

area of rectangle =12B=12xxsqrt33 ≈ 68.93" square units "

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