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 #8 #, #5 #, and #22 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-12-05T11:15:04

The rectangle's area is #137.39# sq.unit.

In right triangle hypotenuse #A=8# and one leg #C=5 #

We know in right triangle #A^2=B^2+C^2 :. B^2= A^2-C^2# or

#B^2=(A+C)(A-C) or B^2=(8+5)(8-5)=39 #

#:. B=sqrt39~~6.245#. So in rectangle, adjacent sides are

#B~~6.245 and D=22# . The area of rectangle is #A_r= B*D# or

#A_r= 6.245*22 ~~ 137.39(2dp)# sq.unit

Rectangle's area is #137.39(2dp)# sq.unit [Ans]