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 #4 #, #2 #, and #5 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-12-22T11:17:58

Area of rectangle is #17.32# sq.unit.

Hypotenuse #A=4 ; C=2# and adjacent to side #B#, the

side of rectangle #D=5#

We know in a right triangle #A^2=B^2+C^2; A=4 ,C=2#

#:.4^2= B^2+2^2 or B^2=16-4=12 :. B=sqrt12=2sqrt3#

Area of rectangle is #A_r=B*D ; D=5:. A_r=2sqrt3*5#

#:. A_r=10sqrt3 ~~ 17.32(2dp)# sq.unit.

Area of rectangle is #17.32# sq.unit. [Ans]