Use the appropriate formula to solve the problem

Question

The length of a rectangular billboard is 7 inches more than the width. The perimeter of the billboard is 138 inches. Find the width of the billboard

Answer 1

Hi Ayanna,

This problem can be solved by creating an equation and solving it to find the width of the billboard.

Let's use the variable w to represent the width of the billboard.

Then we can write the following expression to represent the length of the billboard: w + 7

Since the perimeter of a rectangle can be calculated by adding 2 times the length to 2 times the width , we can write the following equation for the perimeter (P) of the billboard:

P = 2 • length + 2 • width

138 = 2 • (w + 7) + 2 • w

Now use the distributive property, combining like terms, and inverse operations to determine the value of w:

138 = 2w + 14 + 2w

138 = 4w + 14

138 - 14 = 4w + 14 - 14

124 = 4w

124/4 = 4w/4

31 = w

The width if the billboard is 31 inches.

The length will be 31 + 7 = 38 inches

To verify:

Perimeter = 2 • 38 + 2 •31 = 76 + 62 = 138 inches

Hope this helps Ayanna. Let me know if you have further questions or would like to schedule a lesson (online is available if you prefer). Take care.