Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

The quadratic equation would be;

x2+15x-2=0

Working:

Assuming the area around the painting i. e the frame, has a uniform thickness, then;

Length of painting and frame = 8+x

Breadth of painting and frame = 7+x

The area from above step gives;

A = LxW

A = (8+x) (7+x)

On expanding, 56+8x+7x+x2

On simplifying,

56+15x+x2. This should be equal to 58.

58=x2+15x+56

Taking 58 to the other side,

x2+15x-2=0

7 times 8 = 56.

58 - 56 = 2