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 #7 #, #2 #, and #9 #, respectively. What is the rectangle's area?
1 Answer
Mar 25, 2016
≈ 60.374 square units
Explanation:
The area of the rectangle = 9B , where B has to be found.
Since the triangle is right , with A the hypotenuse , we can find B using
#color(blue)" Pythagoras' theorem " # then :
# A^2 = B^2 + C^2 rArr B^2 = A^2 - C^2#
# B^2 = 7^2 - 2^2 = 49 - 4 = 45 # now
# B^2 = 45 rArr B = sqrt45 # and area of rectangle = 9B =
# 9xxsqrt45 ≈ 60.374#
