Question

A rectangular park is 60 yards wide and 100 yards long.

Give the length and width of another rectangular park that has the same perimeter but a smaller area.

Width________
Length ________
​

Answer 1

Width: 40 yd

Length: 120 yd

Explanation:

Perimeter and Area of Rectangles

The perimeter of a rectangle is the sum of all four sides, being x and y the dimensions of the rectangle, then the perimeter is

`P=2x+2y=2(x+y)`

The area is

`A=xy`

We know the dimensions of a rectangular park are 60 yards by 100 yards

The perimeter is

`P=2(x+y)=2(60+100)=320\ yd`

We compute the area

`A=xy=60*100=6,000\ yd^2`

We must find another rectangular park with the same perimeter but with a smaller area. Generally, areas are smaller when the proportion between the dimensions are farther apart. For example, let's lower the lowest dimension, we choose 40 yards as x. If we know x=40, we compute y

`2(x+y)=320`

`x+y=160`

`y=160-40=120`

The new area is

`A=40*120=4,800\ yd^2`

The new area is smaller than the original