Two experimental plots of rectangular shape have the same area, the perimeter of the first section is 76 m

Two experimental plots of rectangular shape have the same area, the perimeter of the first section is 76 m and its length is 20 m, what is the length of the second section if its width is less than the width of the first section by 3 m.

Let’s use the formulas for the perimeter and area of ​​a rectangle:

P = a + b + a + b = 2 * (a + b) and S = a * b, where P is the perimeter of the rectangle, S is the area of ​​the rectangle, a is the width of the rectangle, b is the length of the rectangle.

From the perimeter formula, we determine the width of the first section:

a = P / 2 – b = 76 (m) / 2 – 20 (m) = 38 (m) – 20 (m) = 18 (m).

In this case, the width of the second section is less than the width of the first by 3 (m), which means: 18 (m) – 3 (m) = 15 (m).

Let’s calculate the area of ​​the first section: S = 20 (m) * 18 (m) = 360 (m2).

Since the areas of the sections are equal, the area of ​​the second section is also 360 (m2), therefore, the length of the second section is: b = S / a = 360 (m2) / 15 (m) = 24 (m).

Answer: the length of the second section is 24 meters.