Question

Emily wants to hang a painting in a gallery but the painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. The frame must have an equal width of x on each side. Which quadratic equation represents the area of the painting and frame combined?

Answer 1

The width with the frame is 5 + 2x
The length with the frame is 6 + 2x
We use 2x, because there is an x on both sides.
The total area is just multiplying these two:
(5+2x)*(6+2x)

Do you need help expanding this?

Answer 2

yea

Answer 3

ok so we use foil to get:
2x*2x + 6*2x + 5*2x + 5*6
and simplify to get:
4x^2 + 22x + 30

This is the quadratic equation.

Now the fact that they give you the area as 31 gives me the impression there is another part to the problem. =)

Answer 4

thats all she gave me...:/