A rectangle has a length of 18 yards less than 6 times its width. If the area of the rectangle is 528 square yards, find the length of the rectangle

Question

what is the answer?

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 = 528

L = 6W – 18

I would plug the second equation into the first to get

(6W – 18)(W) = 528

6W^2 - 18W  –  528 = 0

W^2 - 3W – 88 = 0

(W - 11)(W + 8) = 0

W = -8 or W = 11, but only W = 11 makes sense in this context since we need a positive value for a dimension

So Width = 11, then Length = 6(11) - 18 = 66 – 18 = 48

Meaning that the dimensions here are 11 feet wide by 48 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 Michael - 

 

You should start this problem by noting that the area of a rectangle is the length times the width.

 

A = (L) (W)

 

A is given as 528 yards.

 

The problem does not give numbers for the length and width but it does say that the length is 18 yards less than 6 times the width. This can be shown mathematically as:

 

L = 6W - 18

 

Using the area equation above, and plugging in the value for L above, you get:

 

528 = (6W - 18) (W)

 

Multiplying out the right side of the equation gives:

 

528 = 6W² - 18W

 

Subtracting 528 from both sides of equation gives: 

 

6W² - 18W -528 = 0

 

Dividing both sides of the equation by 6 gives:

 

W² - 3W - 88 = 0

 

You can factor the left side of the equation which gives:

 

(W - 11) (W + 8) = 0

 

By setting each of the factors to zero (because any number multiplied by zero is zero), you get

 

W - 11 = 0 or W = 11

 

W + 8 = 0 or W = -8

 

Because a dimension cannot be negative, we know that the width is 11.

 

Using the expression above that gives the length as a function of the width, you can then calculate the length.