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 #, #4 #, and #5 #, respectively. What is the rectangle's area?
1 Answer
Apr 3, 2016
≈ 40.31 square units
Explanation:
The area of the rectangle
#color(blue)" = 5B " # Require to find B. Since it is a right triangle we can use
#color(red)" Pythagoras' theorem " # Since side A is the hypotenuse then
# A^2 = B^2 + C^2 # and
# B^2 = A^2 - C^2 = 9^2 - 4^2 = 81 - 16 = 65 # now
# B^2 = 65 rArr B = sqrt65 # so area of rectangle = 5B =
#5xxsqrt65 ≈ 40.31" square units " #
