Question

A square playground is surrounded by a sidewalk on all sides. the sidewalk is 2n+3 yards long on each side of the park.The sidewalk is 0.5 yard wide.what is the perimeter of the playground?write two equivalent expressions for the perimeter of the playground?

Answer 1

`4(2n+2.5)` yards.

`8n+10` yards.

Explanation:

We have been given that a square playground is surrounded by a sidewalk on all sides. The sidewalk is
`2n+3` yards long on each side of the park.

Since side walk is 0.5 yard wide, so each side of playground will be 0.5 less than each side of sidewalk.

`\text{Length of each side of playground}=\text{Length of each side of sidewalk - Width of sidewalk}`

`\text{Length of each side of playground}=2n+3-0.5`

`\text{Length of each side of playground}=2n+2.5`

Since playground is square, so perimeter of playground will be 4 times the length of each side of playground.

`\text{Perimeter of playground}=4(2n+2.5)`

Upon distributing 4 we will get,

`\text{Perimeter of playground}=8n+10`

Therefore, perimeter of playground will be
`4(2n+2.5)` yards or
`8n+10` yards.