Question

A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular. The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards. Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake? Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Explain her mistake. What is the correct formula?

Answer 1

`x^2- 8x - 256=0`

Explanation:

Let the width of the rectangular park = x

b= x

As the area of the park is given to be 256 Sq yards

length
`l=(256)/(x)`

The perimeter of any rectangle is given as

P = 2(length * width )

Hence

`P = 2 ( x + (256)/(x))`

In order to find the perimeter , we need to find the value of x first . In order to find x we have to use the relation which says that length is 8 yards more width of the park.

that is

`(256)/(x)=x+8`

which will give us the quadratic equation. solving that we will get the value of x

Answer 2

A = (P/4)(P/2 - P/4)
= (P/4)^2

Therefore it is a square
Playground
256 yd^2
P least perimeter

256 = (P/4)^2
P/4 = √256
= 16
P = 4*16
= 64

The least fencing is 64 yards.

Hope I helped!