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

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Answer 1 · 2016-10-31T01:57:13

#8sqrt2#

Given a right-angled triangle with sides A,B, and C, and A is the hypotenuse,

#=> A^2=B^2+C^2#
#=> A^2=B^2+7^2#
#=> B= sqrt(9^2-7^2)=sqrt(32)=sqrt(16*2)=4sqrt2#

given the side length of the rectangle adjacent to side B #=2#,
#=># rectangle area #= 4sqrt2*2=8sqrt2=11.31#