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 #12 #, #8 #, and #4 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-09-09T20:11:31

#"Area"_"rectangle" = 16sqrt(5)#

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By the Pythagorean Theorem:
#color(white)("XXX")B=sqrt(12^2-8^2)=sqrt(80)=4sqrt(5)#

The rectangle has sides of length #4# and #4sqrt(5)#
and therefore has an area of
#color(white)("XXX")4xx4sqrt(5)=16sqrt(5) ~~35.78#