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 #6 #, #4 #, and #9 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-07-01T14:07:22

The reqd. Area of rectangle#=18sqrt5~=40.248# sq.unit..

In the given right triangle with hypo.=A, we have, by Pythagoras Theorem, #B^2+C^2=A^2..........(1)#.

#A=6, C=4#...[Given] & #(1) rArr B^2=36-16=20 rArr B=sqrt20=2sqrt5.#

Hence, the reqd. Area of rectangle #=B xx# length of side adjacent to #B##=2sqrt5*9=18sqrt5~=18*2.236~=40.248# sq.unit.