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 9 9, 4 4, and 8 8, respectively. What is the rectangle's area?

1 Answer
Jim G.
Mar 5, 2016

8sqrt65 ≈ 64.5 " square units"8√65≈64.5 square units

Explanation:

To calculate the area of the rectangle , we require to find the length of side B . This can be done usingcolor(blue) " Pythagoras's theorem " Pythagoras's theorem

In the right triangle: A^2 = B^2 + C^2 A2=B2+C2

hence B^2 = A^ 2 - C^2 = 9^2 - 4^2 = 81 - 16 = 65B2=A2−C2=92−42=81−16=65

now B^2 = 65 rArr B = sqrt65 B2=65⇒B=√65

thus area of rectangle = 8xxsqrt65 = 8sqrt65 ≈ 64.5 8×√65=8√65≈64.5

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