Question

Ширина прямоугольного спортзала 18 м, его периметр равен 96 м. Найди длину и площадь.

Answer 1

Ответ:

длина спортзала = 30 м

площадь спортзала = 540 м²

Пошаговое объяснение:

Дано:

b = 18 м - ширина спортзала

P = 96 м - периметр спортзала

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Найти:

a - длину спортзала

S - площадь спортзала

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Решение:

Периметр прямоугольника вычисляется по формуле:

P = 2 · (a + b) = 2a + 2b, где:

а - длина прямоугольника;

b - ширина прямоугольника.

По условию нам известен периметр и известна ширина.

Выразим длину из формулы периметра:

P = 2a + 2b ⇒ 2a = P - 2b ⇒ a = (P - 2b) : 2.

Подставим известные значения в полученную формулу:

a = (96 - 2 · 18) : 2 = (96 - 36) : 2 = 60 : 2 = 30 (м).

Площадь прямоугольника вычисляется по формуле:

S = ab.

Подставим известные значения в формулу:

S = 30 · 18 = 540 (м²)

Answer 2

Problem Analysis

We are given that the width of a rectangular sports hall is 18 meters and its perimeter is 96 meters. We need to find the length and area of the sports hall.

Finding the Length

To find the length of the sports hall, we can use the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2 * (Length + Width)

We are given that the width is 18 meters and the perimeter is 96 meters. Substituting these values into the formula, we can solve for the length:

96 = 2 * (Length + 18)

Simplifying the equation:

48 = Length + 18

Length = 48 - 18

Length = 30 meters

Therefore, the length of the sports hall is 30 meters.

Finding the Area

To find the area of the sports hall, we can use the formula for the area of a rectangle, which is given by:

Area = Length * Width

We have already found the length to be 30 meters and the width is given as 18 meters. Substituting these values into the formula, we can calculate the area:

Area = 30 * 18

Area = 540 square meters

Therefore, the area of the sports hall is 540 square meters.

Summary

- The length of the rectangular sports hall is 30 meters. - The area of the sports hall is 540 square meters.

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