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. In a different plan, the sides can be of any length as long as the rectangular area remains 256 square yards. What dimensions of the rectangular area provide the least perimeter of fencing? a0 yards and a1 yards

Answer 1

To have a minimum perimeter the area needs to be a square
so a0 = sqrt 256 = 16 yards
and a1 = 16 yards

Answer 2

Answer: Two sides would be

a₀ = 16 yards

a₁ = 16 yards

Explanation:

Since we have given that

Area of playground = 256 sq. yards

We need to find the dimensions of the rectangular area provides the least perimeter of fencing.

Since we know that square is a special kind of rectangle providing least perimeter with same area.

As we know the formula for Square :

`Area=Side^2\\\\256=Side^2\\\\√(256)=Side\\\\16\ yards=Side`

Hence, two sides would be

a₀ = 16 yards

a₁ = 16 yards