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]

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