The perimeter of a rectangle is 256 units. The longer sides are each 12 units more than the shorter sides. What is the length of each side?

Given the numerical statement:

The perimeter of a rectangle is 256 units. The longer sides are each 12 units more than the shorter sides.

Determine the length of each side.

Formula for the Perimeter of the rectangle:

P = 2 ( l + w)

Solution:

Let x = shorter sides

12 + x = longer sides

Substitute the given values of the shorter side, longer side and the perimeter of the rectangle to the formula.

P = 2 ( l + w ) 

256 = 2 ( x + 12 + x)

256 = 2 ( 2x + 12)

Multiply 2 to each value inside the parenthesis, and solve for x.

256 = 4x + 24

Transpose 24 on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

256 - 24 = 4x

232 = 4x

Divide both sides by 4 in order to cancel out 4x, leaving behind x.

232/4 = 4x/4

x = 58

x + 12  = 70

Shorter side = 58

Longer side  = 70

Final answer:

Shorter side = 58

Longer side  = 70