Question

A rectangular park is 50 meters wide and 90 meters long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.

Answer 1

`l = 100\,m` and
`w = 40\,m`

Explanation:

The formulas for the area and perimeter of a rectangle are, respectively:

`A = w\cdot l`

`p = 2\cdot (w + l)`

The perimeter is equal to:

`p = 2\cdot (50\,m + 90\,m)`

`p = 280\,m`

Area is likewise equal to:

`A = (50\,m)\cdot (90\,m)`

`A = 4500\,m^(2)`

Then, equations are now described:

`A = w \cdot l`

`140\,m = w + l`

Likewise, the equation of area is simplified afterwards:

`A = (140\,m - l)\cdot l`

`A = 140\cdot l - l^(2)`

The area is reduced inasmuch as length is increased. Let assume that length is 100 meters. The length and width are described herein:

`l = 100\,m` and
`w = 40\,m`