Calculate the area of a rectangle, its example is 20 m, and the length of one side is 4 times the length of the other side.

Let’s apply the formula for determining the area and perimeter of a rectangle: S = a * b and P = 2 * (a + b), where S is the area of ​​the rectangle, P is the perimeter of the rectangle, a is the length of the rectangle, b is the width of the rectangle.

Let’s take for x (m) – the length of the rectangle, then (4 * x) (m) – the width of the rectangle.

Substitute the values ​​P = 20 (m), a = x (m) and b = 4 * x (m) into the formulas:

S = x * 4 * x,

20 = 2 * (x + 4 * x).

Let’s solve the system of equations.

S = 4 * x2,

20 = 2 * 5 * x.

Wherein:

S = 4 * x2,

20 = 10 * x.

Let’s find the value of the variable x from the second equality:

10 * x = 20,

x = 20/10 = 2 (m).

Let’s substitute in the first equality: S = 4 * 22 = 4 * 4 = 16 (m2).

Let’s check, for this we substitute the values ​​of the sides a = 2 (m) and b = 4 * 2 = 8 (m) into the perimeter formula:

P = 2 * (2 (m) + 8 (m)) = 2 * 10 (m) = 20 (m) – coincides with the condition of the problem.

8 (m) / 2 (m) = 4 times – one side is 4 times larger than the other.

Answer: The area of ​​the rectangle is 16 square meters.