The perimeter of a playing field for a certain sport is 312 ft. The length is 40 ft longer than the width. Find the dimensions

Question

help!! very confusing

Answer 1

Let:

width=W

length=L=W+40.....prob statement

 

The formula for perimeter is....

    P=2x(L+W)

312=2(W+40+W).....substitute for L

312=2(2W+40)........combine like terms

312=4W+80............distribute

232=4W..................subtract 80 from both sides

  58=W....................divide both sides by 4

   W=58

 

Now substitute into expression for L...

L=W+40=58+40=98

...and substitute into the perimeter formula...

    P=2x(L+W)

312=2x(98+58)

312=2(156)

312=312......check√, your solution is correct. 

                    ALWAYS CHECK YOUR WORK!

 

So the field dimensions are 98ft x 58ft.

 

Answer 2

Let length be L and width be W

Given: 2L+2W=312

Given L=40+W ft

2(40+W)+2W=312

80+2W+2W=312

4W=312-80

W=232/4=58

L=58+40=98