Question

Ширина прямоугольника на 9 дм меньше его длины. Если длину увеличить на 2 дм, а ширину на 3 дм, то площадь увеличится на 83 дм квадратных.. Найдите площадь треугольника. Заранее спасибо

Answer 1

Пусть х ширина прямоугольника. Тогда его длина х+9, а площадь х(х+9)
 после увеличения длина станет х+11, ширина х+3, а площадь (х+11)(х+3)
получаем уравнение
(х+11)(х+3)-x(x+9)=83
x²+3x+11x+33-x²-9x=83
5x+33=83
5x=50
x=10
площадь прямоугольника равна 10*(10+9)=190 дм²
 

Answer 2

Problem Analysis

We are given a rectangle with a width that is 9 dm less than its length. If we increase the length by 2 dm and the width by 3 dm, the area of the rectangle increases by 83 square dm. We need to find the area of the triangle.

Solution

Let's assume the length of the rectangle is L dm. According to the problem, the width of the rectangle is 9 dm less than the length, so the width is L - 9 dm.

When we increase the length by 2 dm, the new length becomes L + 2 dm. Similarly, when we increase the width by 3 dm, the new width becomes L - 9 + 3 = L - 6 dm.

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

According to the problem, the area of the rectangle increases by 83 square dm when we increase the length by 2 dm and the width by 3 dm. So we can write the equation:

(L + 2) × (L - 6) - L × (L - 9) = 83

Simplifying the equation:

L^2 - 4L - 12 - L^2 + 9L = 83

Combining like terms:

5L - 12 = 83

Solving for L:

5L = 95

L = 19

Now that we have the length of the rectangle, we can find the width by subtracting 9 from the length:

Width = L - 9 = 19 - 9 = 10

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

Area = 19 × 10 = 190 square dm

Answer

The area of the triangle is 190 square dm.