Question

Если каждую сторону земельного участка, имеющего форму квадрата, уменьшить на 2 метра, то получится участок, площадь которого будет меньше площади первоначального на 16 метров квадратных. найдите стороны первоначального участка

Answer 1

Был квадрат ос стороной х м  с площадью х²  м²
стал квадрат со стороной   (х -2)м   с площадью (х -2)²
по условию:
х² - (х -2)² = 16
х² - х² + 4х - 4 = 16 
4х = 20
х = 5(м) - первоначальная сторона квадрата

Answer 2

Problem Analysis

We are given a square-shaped land plot, and if we decrease each side of the plot by 2 meters, the resulting plot will have an area 16 square meters smaller than the original plot. We need to find the sides of the original plot.

Solution

Let's assume the side length of the original plot is x meters. According to the problem, if we decrease each side by 2 meters, the resulting plot will have an area 16 square meters smaller than the original plot.

The area of the original plot is given by x^2 square meters. The area of the resulting plot is given by (x-2)^2 square meters.

According to the problem, the area of the resulting plot is 16 square meters smaller than the area of the original plot. Therefore, we can set up the following equation:

x^2 - (x-2)^2 = 16

Simplifying the equation:

x^2 - (x^2 - 4x + 4) = 16

x^2 - x^2 + 4x - 4 = 16

4x - 4 = 16

4x = 20

x = 5

Therefore, the side length of the original plot is 5 meters.

Answer

The sides of the original land plot are 5 meters each.

Explanation

By solving the equation x^2 - (x-2)^2 = 16, we find that the side length of the original plot is 5 meters. This satisfies the condition that if we decrease each side by 2 meters, the resulting plot will have an area 16 square meters smaller than the original plot.

Example

Let's verify the solution with an example. If the side length of the original plot is 5 meters, then the area of the original plot is 5^2 = 25 square meters. If we decrease each side by 2 meters, the resulting plot will have sides of length 3 meters, and the area of the resulting plot will be 3^2 = 9 square meters. The difference in area between the original plot and the resulting plot is 25 - 9 = 16 square meters, which matches the given condition.

Therefore, the solution is correct.