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

Answer:

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

Step-by-step 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 $w = 40\,m$