Question

A piece of posterboard has a perimeter of 140 in. If 7 in. are cut off the width, the length becomes four times the width. What are the dimensions of the original piece of posterboard?

Answer 1

To find the dimensions of the original piece of posterboard, we can set up a system of equations. The dimensions of the original piece of posterboard are 36 inches by 9 inches.

Step-by-step explanation:

To find the dimensions of the original piece of posterboard, we can start by setting up a system of equations. Let's assume the original width is w inches. The length of the original piece of posterboard will then be 4w inches.

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. In this case, we have P = 140 inches.

Since 7 inches are cut off the width, the new width becomes w - 7. And since the length becomes four times the width, the new length can be expressed as 4(w - 7).

Using the formula for the perimeter, we can set up the following equation:

2(4(w - 7) + (w - 7)) = 140.

Simplifying the equation, we get 10w - 28 = 70. Solving for w, we find w = 9. Therefore, the dimensions of the original piece of posterboard are 36 inches by 9 inches.