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?
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
