Word problem

Question

A rectangular yard has a width-to-length ratio of 5:9. If the distance around the yard is 2800 ft, what are the dimensions of the yard? 

Answer 1

A ratio of 5:9 means the width divided by the length will equal 5 divided by 9.  We can rewrite this fact as an equation:

 

W = 5

 L     9     We can cross multiply this equation and solve for either one of the variables:

 

9W = 5L  Solve for L:    9W = L

                                    5

 

We also know the distance around the perimeter of the yard is 2,800 feet.  To get around the yard, we walk the length of the yard two times and the width of the yard two times. So the distance we walk around the yard is:

 

2W + 2L = 2800

 

Substitute 9W for L and solve for W:     

                 5

2W + 2(9W) = 2800  (Now clear the fraction by multiplying every term by 5.

             5

 

10W + 18W = 14000  (Combine terms)

 

28W = 14000  (Isolate W by dividing by 28)

 

W = 14000   =  500  (Now go back to the original ratio equation to solve for L)

          28

 

L = 9W  =  9(500)  =  9(100)  =  900

        5           5

 

The length of the yard is 900 feet.

The width of the yard is 500 feet.

 

Answer 2

W:L = 5:9

 

W/L = 5/9

 

W = 5/9 *L

 

Perimeter = 2(W+L)

 

2(W+L) = 2800

 

2(5/9*L + L) = 2800

 

L(1+5/9) = 1400

 

14/9 * L = 1400

 

L = 900

 

W = 5/9 * 900 = 500

 

Hence the dimensions are Length = 900ft and Width = 500ft