Question

A rectangular photograph is 7 inches long and 6 inches wide. The photograph is framed using a material that is x inches wide. If the area of the frame and photograph combined is 156 square inches, what is the width of the framing material

Answer 1

The width of the framing material is 3 inches

Explanation:

we know that

The area of the frame and photograph combined is given by the expression

`156=(7+2x)(6+2x)`

solve for x

Expanded the expression

`156=42+14x+12x+4x^2\\4x^2+26x+42-156=0`

`4x^2+26x-114=0`

solve the quadratic equation by graphing

using a graphing tool

The solution is x=3 in

see the attached figure

therefore

The width of the framing material is 3 inches