Question

Вариант 2 Задания 1. Стороны прямоугольника равны 6см и 20 см. а) Найдите ширину прямоугольника, равновеликого данному, если его длина равна 30см. провели диагональ. Будут ли ОНИ b) B каждом ИЗ этих прямоугольников равносоставленными? Ответ обоснуйте. 131

Answer 1

Ответ:

6+20+30 это всё и да учи матешу

Answer 2

Finding the Width of the Rectangle

To find the width of the rectangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the length and the width of the rectangle form the two sides of a right-angled triangle, and the diagonal is the hypotenuse.

Using the Pythagorean theorem, we can calculate the width of the rectangle as follows:

Step 1: Calculate the square of the diagonal: - \( \text{Diagonal}^2 = \text{Length}^2 + \text{Width}^2 \)

Step 2: Substitute the given values: - \( 30^2 = 6^2 + \text{Width}^2 \) - \( 900 = 36 + \text{Width}^2 \)

Step 3: Solve for the width: - \( \text{Width}^2 = 900 - 36 \) - \( \text{Width}^2 = 864 \) - \( \text{Width} = \sqrt{864} \) - \( \text{Width} \approx 29.39 \, \text{cm} \)

So, the width of the rectangle, if its length is 30 cm and the sides are in the same proportion, is approximately 29.39 cm.

Comparing the Rectangles

To determine if the rectangles are similar, we can compare the ratios of their corresponding sides. Two rectangles are similar if their corresponding sides are in proportion.

The ratio of the sides of the given rectangle is: - \( \frac{20}{6} = \frac{10}{3} \)

The ratio of the sides of the rectangle with a length of 30 cm and a width of approximately 29.39 cm is: - \( \frac{29.39}{30} \approx 0.98 \)

Since the ratio of the sides of the two rectangles is not equal, the rectangles are not similar.

Therefore, the rectangles are not similar because their corresponding sides are not in the same proportion.

I hope this helps! If you have further questions, feel free to ask.