A garden plot with an area of 8 acres (800m2) is surrounded by a fence, the length of which is 120m.

A garden plot with an area of 8 acres (800m2) is surrounded by a fence, the length of which is 120m. Find the length and width of the patch.

The plot is surrounded by a fence. The area of ​​the site and the length of the fence are known. Let’s find the length and width of the site.

To begin with, we note that the length of the fence installed around the site determines the perimeter of the site.

The plot has a rectangular shape.

The area of ​​a rectangle is the product of length and width.

The perimeter of a rectangle is twice the sum of its length and width.

We introduce variables.

Let a be one side of the lot and b the second side of the lot. Let’s compose and solve a system of two equations with two unknowns:

2 * (a + b) = 120;

a * b = 800;

a + b = 600;

b = 60 – a;

a * (60 – a) = 800;

60 * a – a ^ 2 = 800;

a ^ 2 – 60 * a + 800 = 0;

a1 = 40;

a2 = 20;

The sides of the site are 40 and 20 m.