Question

Сторону квадрата увеличили на 30%. На сколько процентов 1) увеличился его периметр; 2) увеличилась его площадь?

Answer 1

Пусть а - сторона квадрата.

1) Периметр квадрата равен Р=4а.

После увеличения на 30% длина стороны квадрата станет равна а+0,3а=1,3а

Тогда новый периметр Р' =4·1,3а=1,3·(4а) = 1,3·P.

То есть периметр увеличится также на 30%.

2) Площадь квадрата S=а².

После увеличения стороны квадрата на 30% новая площадь

S' = (1,3a)²= 1,69·а² = 1,69·S.

То есть площадь увеличится уже на 69%.

Answer 2

To solve this problem, let's assume the original side length of the square is "x."

1. Increase in Perimeter: When the side length of the square is increased by 30%, the new side length will be:

New side length = x + 0.30x = 1.30x

The perimeter of the original square is 4x (since all sides are equal). And the perimeter of the new square is 4 times the new side length:

New perimeter = 4 * (1.30x) = 5.20x

Now, to find the percentage increase in the perimeter, we can use the formula:

Percentage increase = [(New Value - Original Value) / Original Value] * 100

Percentage increase in perimeter = [(5.20x - 4x) / 4x] * 100 = (1.20x / 4x) * 100 = 30%

So, the perimeter increased by 30%.

2. Increase in Area: The area of the original square is x^2 (side length multiplied by side length). And the area of the new square with increased side length will be:

New area = (1.30x)^2 = 1.69x^2

Now, to find the percentage increase in the area, we can use the same formula as before:

Percentage increase = [(New Value - Original Value) / Original Value] * 100

Percentage increase in area = [(1.69x^2 - x^2) / x^2] * 100 = (0.69x^2 / x^2) * 100 = 69%

So, the area increased by 69%.

In summary, when the side length of the square is increased by 30%:

1. The perimeter increased by 30%.
2. The area increased by 69%.