Question 233734
A recreation department plans to build a rectangular playground enclosed by 1000 meters of fence. If the length of the playground is 4 meters less than 3 times the width find the length and width of the playground.

L = length of the playground
W = width of the playground.

Perimeter of the playground is 1000 meters.


P = Perimeter of the playground.


P = 2L + 2W


1000 = 2L + 2W


Length of the playground is 4 meters less than 3 times the width.


L = 3*W - 4


Replace L with 3*W-4 to get:


1000 = 2L + 2W becomes:


1000 = 2 * (3W-4) + 2W which becomes:


1000 = 6W - 8 + 2W which becomes:


1000 = 8W - 8


Add 8 to both sides to get:


1008 = 8W


Divide both sides by 8 to get:


W = 126


If W = 126, then:


L = 3*W - 4 = 374


P = 1000 = 2L + 2W = 2*374 + 2*126 = 1000


L = 3*W - 4 = 3*126 - 4 = 374 is ok.


Perimeter equals 1000.
L = 3W - 4


Everything looks good so the answer is:


L = 374
W = 126