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

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Answer 1 · 2017-12-05T11:15:04

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

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

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]

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 88 , 5 55 , and 22 2222 , respectively. What is the rectangle's area?