A room has an area of 60 square meters and a perimeter of 32. What are the length and width of the room?

The dimensions of the room would be 10 x 6

Step-by-step explanation:

In order to find this, start with the perimeter formula and solve for either variable.

P = 2L + 2W

32 = 2L + 2W

2L = 32 - 2W

L = 16 - W

Now we input that into the L part of the area equation.

A = LW

60 = LW

60 = (16 - W) W

60 = 16W - W^2

W^2 + 60 = 16W

W^2 - 16W + 60 = 0

Now we can factor this.

(W - 10) (W - 6)

And to solve we set each parenthesis equal to 0

W - 10 = 0

W = 10

W - 6 = 0

W = 6

So we know these are the two possible dimensions.