A rectangular red sticker has a perimeter of 46 millimeters and an area of 120 square millimeters. What are the dimensions of the sticker

Question

The formatting is __millimeters by __millimeters

Answer 1

Hi Shannon, What a great question!

Let's call the dimensions of the rectangle L (length) and W (width).

The first step is to create an equation using L and W to represent the perimeter. Then create an equation using L and W to represent the area of the rectangle. It also might help to sketch a rectangle and label the 4 sides with L, W, L, W.

Perimeter: L + L + W + W = 46

Area: L x W = 120

Anytime you have two equations and two variables, you can solve!

Let's do a little bit of work to the perimeter equation first:

L + L + W + W = 46

Combine like terms: 2L + 2W = 46

Divide each term by 2: L + W = 23

So, now the two equations are:

L + W = 23

and

L x W = 120

Depending on whether or not you have learned how to "factor polynomials" which involve x^2 ("x squared" or "x to the power of 2") there are a few ways to solve this system of equations from here.

I am going to explain a simpler method:

If you assume that L and W are each whole numbers (which they might not be, but let's try!), you can actually solve this quite simply by creating a list of factor pairs for 120. What are pairs of numbers that when you multiply them you arrive at 120? For example: 12 x 10 = 120. This means that there is a chance that L is 12 and W is 10. However, if you substitute those values into L + W = 23, 12 + 10 does not equal 23.

Try out some other factor pairs that have a product of 120 and then when you add those two values you get a sum of 23! Good luck!