Question

You finally made it has arrived! Your parents are so proud that they are throwing you a HUGE party. They have rented a big tent for your graduation party just in case it rains. The inside of the tent (represented by the blue area) is set up for a dance floor for you and friends to dance the night away.

The rectangular dance floor is twice as long as it is wide. The tent surrounds the dance floor, leaving some space (7 feet in each direction) for guests to mingle and cool off after dancing. This extra space (represented by the grey area) has an area of 952 square feet. Your task is to find the dimensions of the dance floor. Be sure to show all work.
Dimensions Outside:Top= 2x+14
Side=x+14

Gray Area= 952 ft.^2

Dimensions Dance Floor:Top=2x
Side= x

Answer 1

The area of the whole tent can be described as: (2x +14)(x+14) = 2x^2 + 28x + 14x + 196 = 2x^2 + 42x + 196. The area of the dance floor is: x * 2x = 2x^2. We know that the area of the gray area is 952, and that it is equal to the area of the whole tent minus the area of the dance floor. So we know that 952 = (2x^2 + 42x +196) - 2x^2. This can be simplified to 952 - 196 = 42x, and 18 = x. Since x = 18 and the area of the dance floor is 2x^2, the area = 2 * 18^2 = 648. So the dance floor is 18 feet by 36 feet with an area of 648 square feet.