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 8 8, 7 7, and 2 2, respectively. What is the rectangle's area?

1 Answer
Jim G.
Mar 17, 2016

≈ 7.746 square units

Explanation:

The area of the rectangle = 2B . To calculate the area require to find B.
Since the triangle is right , with A the hypotenuse then using color(blue)" Pythagoras' theorem " "will enable B to be calculated. " Pythagoras' theorem will enable B to be calculated.

hence : A^2 = B^2 + C^2 rArr B^2 = A^2 - C^2 A2=B2+C2⇒B2=A2−C2

B^2 = 8^2 - 7^2= 64-49 = 15 rArr B = sqrt15 B2=82−72=64−49=15⇒B=√15

and area of rectangle 2B = 2xxsqrt15 ≈ 7.746" square units "2B=2×√15≈7.746 square units

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