A rectangular bathroom mirror has a perimeter of 22 feet. Its area is 30 square feet. What are the dimensions of the mirror?

6 feet long and 5 feet wide.

Explanation:

Given that the formula for area is:

A=Length x Width

And perimeter is:

P = 2L + 2W

We know area is 30 and perimeter is 22, so our equations are:

30 = L * W

22 = 2L + 2W

To solve as a system of equations, lets isolate L on the second equation.

22 = 2L + 2W

22 - 2W = 2L

Divide both sides by 2

11 - W = L

Inserting it into the first equation

30 = (11 - W) W

30 = 11W - W²

This looks like a quadratic, so let's bring everything to the left side and factor.

W² - 11W + 30 = 0

(W - 6) (W - 5) = 0

W = 6 or W = 5

Insert both of these into 30 = L*W to find L

30 = 6L

L = 5 when W = 6

or 30 = 5L

L = 6 when W = 5

Hence, the mirror is 6 feet long and 5 feet wide.