the perimeter of a basketball court is 282 ft the length is 41 ft longer than the width find the dimensions of the court

Question

the perimeter of a basketball court is 282 ft the length is 41 ft longer than the width find the dimensions of the court

Answer 1

Perimeter = P = 282

 

Width = W

Length = L = 41 + W

 

Set up your equation.

P = 282 = 2L + 2W

 

Plug in and simplify.

 

      282 = 2*(41 + W) + 2W

      282 = 82 + 2W + 2W

      282 = 82 + 4W

      282 -82 = 82 + 4W - 82

      200/4 = 4W/4

      W = 50

 

Plug your value for W in to find L.

L = 41 + 50 = 91

 

Based on this, you know your court is 91 ft X 50 ft, with Width = 50ft and Length = 91ft

Answer 2

This is solved by manipulating the perimeter formula. You know that the length is 41 ft longer than the width, which can be expressed as l=w+41. You also know the value of the perimeter, 282 ft. Plugging this information into the perimeter formula and solving for w:

 

P=2l+2w

282=2(w+41)+2w

282=2w+82+2w

282=4w+82

200=4w

w=50 ft.

 

So, the width is 50 ft. With this in mind, plug it back into your length equation and:

 

l=w+41

l=50+41

l=91

 

So, the length is 91 ft.

 

To check, plug these values back into the perimeter formula and you should get the final value given in the problem:

 

P=2l+2w

P=2(91)+2(50)

P=182+100

P=282