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 #8 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-10-09T00:47:09

#Area_("rectangle") = 24sqrt5 approx 53.67#

Draw the figure to better understand the problem:
enter image source here

To find the area of the rectangle, find the side length of B first.

#B^2 + 2^2 = 7^2#

#B^2 = 7^2 - 2^2#
#B^2 = 49-4 = 45#
#B =sqrt(45)#

#B = 3sqrt5#
#" "B approx 6.71#

#Area_("rectangle") = 8*3sqrt5#

#Area_("rectangle") = 24sqrt5 approx 53.67#