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 :

xero099

Answer:

[tex]l = 100\,m[/tex] and [tex]w = 40\,m[/tex]

Step-by-step explanation:

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

[tex]A = w\cdot l[/tex]

[tex]p = 2\cdot (w + l)[/tex]

The perimeter is equal to:

[tex]p = 2\cdot (50\,m + 90\,m)[/tex]

[tex]p = 280\,m[/tex]

Area is likewise equal to:

[tex]A = (50\,m)\cdot (90\,m)[/tex]

[tex]A = 4500\,m^{2}[/tex]

Then, equations are now described:

[tex]A = w \cdot l[/tex]

[tex]140\,m = w + l[/tex]

Likewise, the equation of area is simplified afterwards:

[tex]A = (140\,m - l)\cdot l[/tex]

[tex]A = 140\cdot l - l^{2}[/tex]

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

[tex]l = 100\,m[/tex] and [tex]w = 40\,m[/tex]

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