Question

A window is twice as long as it is wide. The area of the window is 2x where x

is the width of the window. The window is surrounded by a frame that is 2 inches
on all sides. The area of the window and frame is 2x2 + 12x +16.
What is the area of the window frame?

Answer 1

When we have a rectangle of length L and width W, the area is calculated as:

A = W*L

In this case, W = x, and the area is:

A = 2*x

Then we must have L = 2.

We know that the area of the window and the frame (together) is:

a = 2*x^2 + 12*x + 16

The area of the frame alone, will be equal to the difference between the area of both objects (a) and the area of the window alone (A)

area of the frame = a - A

= (2*x^2 + 12*x + 16) - (2*x) = (2*x^2 + 10*x + 16)

This is the area of the frame