This 2080 square meter rectangular piece of land is surrounded by a 184 meter long hedge.

This 2080 square meter rectangular piece of land is surrounded by a 184 meter long hedge. Find the length and width of the plot.

The hedge that encloses a plot of land is the perimeter of this plot.

Let’s find the sum of the sides.

To do this, divide the length of the fence into 2 equal parts.

We get:

184/2 = 92 m.

Let’s say the length is x and the width is y.

We get the system:

x + y = 92.

x * y = 2080.

We express x.

x = 92 – y.

Substitute the found x value into the second equation.

y * (92 – y) = 2080.

92 * y – y ^ 2 – 2080 = 0.

y ^ 2 – 92 * y + 2080 = 0.

D ^ 2 = (-92) ^ 2 – 4 * 1 * 2080 = 8464 – 8320 = 144.

D = √144 = 12.

y = (92 + 12) / 2 = 104/2 = 52 m.

x = 92 – 52 = 40 m.

Answer:

52 and 40 meters.