# 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 9 , 3 , and 2 , respectively. What is the rectangle's area?

The area of the rectangle is $12 \sqrt{2} s q . u n i t$
In right angle triangle sides, $A = 9 , C = 3 \therefore B = \sqrt{{9}^{2} - {3}^{2}} = \sqrt{72} = 6 \sqrt{2}$. So the sides of rectangle are $6 \sqrt{2} , 2 , 6 \sqrt{2} , 2 \therefore$ The area of the rectangle is ${A}_{r} = 2 \cdot 6 \sqrt{2} = 12 \sqrt{2} s q . u n i t$[Ans]