Question

The perimeter of a square box is 12x+32. Write an equivalent expression that shows the perimeter as four times the side length of the box.

Answer 1

Answer: $4(3x+8)$

The perimeter of a square is the sum of each of its four sides. If each side is $L$:

$P_{square}=L+L+L+L$

Which is the same as:

$P_{square}=4L$    (1)

In this case we are told that the perimeter of a square box is:

$P_{square}=12x+32$    (2)

Or:

$4L=12x+32$    (3)

If we want to find the equivalent expression as it was asked, we firstly have to find the value of one side $L$ from (3):

$L=\frac{12x+32}{4}$    (4)

Simplifying by the common factor:

$L=\frac{4(3x+8)}{4}$    (4)

$L=3x+8$>>>>>This is the value of each side of the square box

Now, equivalent expression that shows the perimeter as four times the side length of the square box, is four times $L$:

$4L=4(3x+8)$