Question

Из прямоугольного листа фанеры вырезали квадратную пластинку, для чего с одной стороны листа фанеры отрезали полосу 2 см, а с другой, соседней, 3 см. Найдите сторону получившегося квадрата, если известно, что его площадь на 51 см² меньше площади прямоугольника.

Answer 1

х -длина

у -ширина

х*у-(х-3)(у-2)=51

х-3=у-2, решаем систему

2х+3у=57

х=у+1

2у+2+3у=57

5у=55

у=11

х=12

Answer 2

Finding the Side Length of the Square Cut from a Rectangular Plywood Sheet

To find the side length of the square cut from the rectangular plywood sheet, we can use the information provided about the dimensions of the cuts and the difference in area between the square and the original rectangle.

Given: - A rectangular plywood sheet. - A square plate cut from the plywood sheet. - From one side of the plywood sheet, a strip of 2 cm was cut. - From the adjacent side of the plywood sheet, a strip of 3 cm was cut. - The area of the square is 51 cm² less than the area of the original rectangle.

Solution:

Let's denote the length of the original rectangle as L and the width as W. The area of the original rectangle is then given by L × W.

The area of the square is given as 51 cm² less than the area of the original rectangle, so we have the equation:

L × W - 51 = side_length_of_square × side_length_of_square

We also know that the length and width of the original rectangle are reduced by 2 cm and 3 cm, respectively, due to the cuts. Therefore, the new length and width of the rectangle are (L - 2) and (W - 3).

From the given information, we can set up the following equation:

(L - 2) × (W - 3) - 51 = side_length_of_square × side_length_of_square

Solving these equations will give us the side length of the square.

Let's calculate the side length of the square using the provided information.