Question

Francesca wants to glue this 3-inch by 5-inch photo on top of a mat that will increase the length of each side by another x inches. Find an expression representing the area of the mat and use this expression to find the area and cost of the mat for different values of x.

Answer 1

The photo along with the mat will be something like this:

So, new side length = 3 + 2x

new height = 5 + 2x

Hence,

Rectangle Area (A) = length * height

Thus,

`\begin{gathered} A=(3+2x)(5+2x) \\ A=15+6x+10x+4x^2 \\ A=15+16x+4x^2 \end{gathered}`