A rectangular piece of land with an area of 3200 m2 is surrounded by a fence 240

A rectangular piece of land with an area of 3200 m2 is surrounded by a fence 240 meters long. Find the length and width of this area.

Suppose the length of the section is x meters and the width is y.

In this case, the perimeter equation will be:

x + y + x + y = 240.

2 * (x + y) = 240.

x + y = 120.

The area of the site will be:

x * y = 3200.

Express the length of a rectangular piece of land from the first equation.

x = 120 – y.

Substitute x into the second equation:

y * (120 – y) = 3200.

120 * y – y ^ 2 – 3200 = 0.

y ^ 2 – 120 * y + 3200 = 0.

By Vieta’s theorem, we get:

x = 80 m.

y = 40 m.

Answer:

The length of the section is 80 meters, the width of the section is 40 meters.