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

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Answer 1 · 2017-06-08T10:27:50

Area of rectangle is #16sqrt2# sq.unit.

The sides of right triangle are hypotenuse ,#A=6 ,C=2 ; B= ? #

We know #A^2=B^2+C^2 :. B^2= A^2-C^2=36-4=32 :. B= sqrt32=4sqrt2#

Now we have two adjacent sides of rectangle as #B=4sqrt2 and D=4 #

Area of rectangle is #A_r=B*D=4sqrt2*4=16sqrt2# sq.unit [Ans]