the length of a rectangle is four time the width. if the area of the rectangle is 16 square inches, what is the length and the width

Question

 The length of a rectangle is four time the width. if the area of the rectangle is 16 square inches, what is the length and the width

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to find a way to relate the quantities of the given rectangle to one another. On this one we have

Area = L x W = 16

L = 4W

I would plug the second equation into the first to get

(4W)(W) = 16

4W^2 = 16

W^2 = 4

W = -2 or W = 2, but only W = 2 makes sense in this context since we need a positive value for a dimension

So Width = 2, then Length = 4(2) = 8

Meaning that the dimensions here are 2 feet wide by 8 feet long

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Mary, the area of a rectangle is given by: L * W = A. Here, L = 4 * W, and the are is 16 square inches.

 

Substitute in: L * W = A:

 

4W * W = 16

 

W² = 4

 

W = ±2

 

We cannot have a negative width, therefore we can discard the W = -2 solution.

 

W = 2

 

L = 4*W, or 8

 

The width of the rectangle is 2 inches.

 

The length of the rectangle is 8 inches.

 

Questions?