Exercise 37 Page 829

One side of a rectangle measures 6 inches and its diagonals measure 56 foot. We want to find its area. We will start by converting 56 foot to inches, which involves using a conversion factor. 12in./1ft Multiplying 56 foot by this conversion factor will convert it to inches. The rectangle's diagonals measure 10 inches. Let's make a diagram of the rectangle with one of the diagonals. The area of a rectangle is calculated by multiplying the rectangle's length times its width. Therefore, we need to find its width. To do so, we will use the Pythagorean Theorem. a^2+ b^2= c^2 In the formula, a and b are the legs and c is the hypotenuse of a right triangle. In our triangle, a= 6 and c= 10. Let's substitute these values into the formula and solve for b. Since a negative side length does not make sense, we only need to consider positive solutions. Finally, to find the area of the rectangle, we will use the following formula and multiply the rectangle's length times its width. A= a * b Let's substitute the measurements a= 6 and b= 8 into the formula to calculate A. The area of the rectangle is 48 square inches.