Question

Help, I'm stuck.

Answer 1

A 50m by 120m park consists of a rectangular lawn surrounded by a path of uniform width. Find the dimensions of the lawn if its area is the same as the area of the path.

Answer 2

first, let x = path width

Answer 3

draw a diagram to help

Answer 4

the area of the lawn is (50-2x)(120-2x) and the path area is (50)(120) - (50-2x)(120-2x)

Answer 5

the area of the lawn is (50-2x)(120-2x) and the path area is (50)(120) - (50-2x)(120-2x)

Answer 6

and since lawn area= path area, solve and you get x= 10 and 75

Answer 7

but 75 is irrelevant so keep x=10 as path width

Answer 8

then just plug back into the dimensions of the lawn and you get the answer, w= 30m andd length = 100 m