Question

Решите пожалуйста задачу : Длина прямоугольника на 12 дм больше его ширины. Если длину увеличить на 3 дм, а ширину – на 2 дм, то площадь его увеличится на 80 дм квадратных. Найдите длину и ширину прямоугольника. Заранее спасибо

Answer 1

Пусть длина х, тогда ширина х-12, площадь- х*(х-12), увеличили длину  и она стала х+3, а ширина х-12+2=х-10, площадь (х+3)*(х-10) разность площадей =80 получим уравнение (х+3)*(х-10)-х*(х-12)=80. корень х=22 -это длина, 10дм-ширина

Answer 2

Problem Analysis

We are given that the length of a rectangle is 12 dm (decimeters) more than its width. When the length is increased by 3 dm and the width is increased by 2 dm, the area of the rectangle increases by 80 square dm. We need to find the length and width of the rectangle.

Solution

Let's assume the width of the rectangle is x dm. According to the problem, the length of the rectangle is 12 dm more than its width, so the length can be expressed as x + 12 dm.

When the length is increased by 3 dm, the new length becomes x + 12 + 3 = x + 15 dm. Similarly, when the width is increased by 2 dm, the new width becomes x + 2 dm.

The area of a rectangle is given by the formula: Area = Length × Width.

According to the problem, when the length is increased by 3 dm and the width is increased by 2 dm, the area of the rectangle increases by 80 square dm. Mathematically, we can express this as:

(x + 15) × (x + 2) - x × (x + 12) = 80

Simplifying the equation:

x^2 + 17x + 30 - x^2 - 12x = 80

5x = 50

x = 10

Therefore, the width of the rectangle is 10 dm.

The length of the rectangle can be found by adding 12 dm to the width: 10 + 12 = 22 dm.

So, the length of the rectangle is 22 dm.

Answer

The width of the rectangle is 10 dm and the length of the rectangle is 22 dm.