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

##### 1 Answer

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. " # hence :

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

# B^2 = 8^2 - 7^2= 64-49 = 15 rArr B = sqrt15 # and area of rectangle

# 2B = 2xxsqrt15 ≈ 7.746" square units "#