Question

A frame that measures 14 inches by 16 inches is of uniform width. The area of the picture inside is 48square inches. What is the width of the frame?

Answer 1

To solve this question we will use the following diagram:

The area of the big rectangle minus the area of the small rectangle is:

$14in\times16in-48in^2=176in^2.$

Since the frame has a uniform width, then:

$16x+16x+(14-2x)x+(14-2x)x=176.$

Solving the above equation for x we get:

$\begin{gathered} 32x+28x-4x^2=176, \\ 15x-x^2-44=0. \\ x^2-15x+44=0, \\ (x-4)(x-11)=0. \end{gathered}$

Then:

$x=4\text{ or x=11,}$

but 11 is not a solution with real meaning, therefore x=4.

Answer: The width is 4 in.