Question

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?

Answer 1

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