Question

The perimeter of a local dog 156 feet. If the length of the park is 2 feet less than 3 times the width, what are the dimensions of the dog park?

Answer 1

Total area is 1160 sq. feet. Length is 58 feet and width is 20 feet.
Total area is 58*20=1160

Explanation:

Since we know that length is 2 less than 3 times of width
and we know that perimeter is [P]
So length is
L= 3W-2

P= 2L + 2W [ that is 2xLength + 2x Width]

156 = 2( 3W-2) + 2 W

Or
`156 = 6 W -4 + 2 W`
Or
`156 = 8W-4`
Or

`8W = 156 + 4`
Or
`8W = 160`

Or
`W = 160/8 = 20`

Hence answer is length is 20 Feet.

Now we can find out the length of park:

`2L = P - 2 W`
`2L = 156 - 2*20`
or
`2L = 156 - 40`
Or
`2L= 116`

Or
`L=116/2=58`

Hence Length is 58 feet

Now again we can verify the answer by determine the perimeter

Since P = 2L+2W
Hence `P=2*58 + 2*20`

Or

`P = 116+40=156`

Or

`P = 156`