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 2 , 2/3 , and 3 , respectively. What is the rectangle's area?

1 Answer
Mar 1, 2016

4sqrt(2)

Explanation:

The area of a rectangle is A = Base*Height The base is given as 3 and the height is B. We can use Pythagoras' Theorem to calculate B because it is a right triangle and we have been given the lengths of the other two sides.

A^2 = B^2 +C^2
B^2 = A^2 - C^2 = 2^2 - (2/3)^2
B^2 = 4 - 4/9 = 32/9

B = sqrt(32/9) = (4sqrt(2))/3

Area A = 3*(4sqrt(2))/3 = 4sqrt(2)