the length of a rectangle is 9 more that the width. the area is 360 square centimeters. Find the length and width

Question

the length of a rectangle is 9 more that the width. the area is 360 square centimeters. Find the length and width

Answer 1

Let width = x

Let length = x + 9

Area = 360

 

The area of a rectangle is

 

length × width

 

 

Set up an equation.

 

x(x + 9) = 360

x² + 9x = 360

 

 

Subtract 360 on both sides of equation to make the right side zero.

 

x² + 9x - 360 = 0

 

Lets use the quadratic formula to save us time from figuring out factors 360 that will give us a sum of 9.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 9

c = -360

 

Plug in these variables into the formula.

 

x = (-9 ± √(81 - 4(-360))) / 2

 

x = (-9 ± √(1521)) / 2

 

x = (-9 ± 39) / 2

 

x = 30 / 2

x = 15

 

x = -48 / 2

x = -24

 

 

We have two values of x.   Accept the positive value of x, since we cannot have a negative dimension.

 

 

Substitute the accepted value of x into the dimensions.

 

width = x = 15

length = x + 9 = 15 + 9 = 24

 

 

The width is 15 cm.

The length is 24 cm.

 

 

Answer 2

Hi Andy!

 

From the first sentence we can write:

 

L = W + 9 

 

From the second sentence we can write:

 

A = L x W = (W + 9) x W = W² + 9W =360 

 

So, W² + 9W - 360 = 0.

 

And W=15 and L=W+9=15+9=24

 

I hope this is helpful.

 

Best regards!