# 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 12 , 8 , and 6 , respectively. What is the rectangle's area?

Dec 24, 2016

53.7

#### Explanation:

It is easiest to work out this type of problem with a drawing. Essentially, we want the rectangle area, which is simply B x 6. So, we only need to calculate B from the triangle.

${A}^{2} = {B}^{2} + {C}^{2}$ ; ${B}^{2} = {A}^{2} - {C}^{2}$

B^2 = 12^2 – 8^2 ; B^2 = 144 – 64 = 80

B = 8.94 ; 8.94 x 6 = 53.7