Question

Ширина прямокутника 7 см , а діагональ 25 см ,знайдіть довжину і периметр прямокутника

Answer 1

Ответ:

24 см

Объяснение:

а - длина прямоугольника

b - ширина прямоугольника

с - диагональ прямоугольника

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b=7 см

с=25 см

а - ? см

Решение:

по теореме Пифагора:  ⇒

⇒

(cм) - длина прямоугольника.

Ответ: 24 см другая сторона прямоугольника.

Answer 2

Finding the Length and Perimeter of a Rectangle

To find the length and perimeter of a rectangle, we need to use the given information about the width and diagonal of the rectangle.

Let's start by using the Pythagorean theorem to find the length of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangle acts as the hypotenuse, and the width and length of the rectangle are the other two sides. So, we can set up the following equation:

width^2 + length^2 = diagonal^2

Given that the width of the rectangle is 7 cm and the diagonal is 25 cm, we can substitute these values into the equation:

7^2 + length^2 = 25^2

Simplifying the equation, we have:

49 + length^2 = 625

Subtracting 49 from both sides, we get:

length^2 = 576

Taking the square root of both sides, we find:

length = 24 cm

Now that we know the length of the rectangle is 24 cm, we can calculate the perimeter. The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given by the formula:

perimeter = 2 * (length + width)

Substituting the values we have, we get:

perimeter = 2 * (24 + 7) = 2 * 31 = 62 cm

Therefore, the length of the rectangle is 24 cm and the perimeter is 62 cm.

Please let me know if there's anything else I can help you with!