Question

The length of one side of a square is (x + 2 1/4). If the perimeter is 14 units, what is the area?

Answer 1

The perimeter is the total of adding all of the side lengths together.

A square has 4 equal side lengths.

So the perimeter of a square is:

P = s + s + s + s  or  P = 4s

[P = perimeter       s = side lengths of the square]

Since you know the side length of the square is (x + 2 1/4), you can replace s with (x + 2 1/4)

P = 4s

P = 4(x + 2 1/4)  Multiply 4 into (x + 2 1/4)

P = 4x + 8 4/4

P = 4x + 9

Since you know the perimeter, you can plug it in.(you could have also plugged it in in the beginning)

P = 4x + 9

14 = 4x + 9  Subtract 9 on both sides

5 = 4x  Divide 4 on both sides

5/4 = x

Now that you know x, find the side length of the square.

(x + 2 1/4)

(5/4 + 2 1/4)

2 6/4 = 3 2/4 = 3 1/2 units or 3.5 units

To find the area of a square, you multiply 2 of the sides together:

A = s · s  

A = 3.5 · 3.5

A = 12.25 units²