SOLUTION: A square park is surrounded by a path of uniform width 2 metres all round it. The area of the path is
288 sq. metres. The perimeter of the park is?
Question 584726: A square park is surrounded by a path of uniform width 2 metres all round it. The area of the path is
288 sq. metres. The perimeter of the park is? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A square park is surrounded by a path of uniform width 2 metres all round it.
The area of the path is 288 sq. metres. The perimeter of the park is?
:
Let x = the length of one side of the park
then
x^2 = the area of the park
and
(x+4) = the overall length of the side including the path
then
(x+4)^2 = the overall area
:
Overall area - park area = path area(288 sq/m)
(x+4)^2 - x^2 = 288
FOIL (x+4)(x+4)
x^2 + 8x + 16 - x^2 = 288
;
Combine like terms, the x^2's cancel out
8x = 288 - 16
x =
x = 34 meters is the side of the park
then
4(34) = 136 meters is the perimeter of the park
:
:
:
Check solution by finding the area of each; Overall side length = 38 m
38^2 + 34^2 =
1444 - 1156 = 288
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