Question

В прямоугольнике диагональ равна 27, периметр 56. Найти площадь.

Answer 1

Х - ширина прямоугольника  
(28 - х) - длина его
Уравнение
По теореме Пифагора находим  диагональ  
х² + (28 - х)² = 27²
х² + 784 - 56х + х² = 729
2 х² - 56х + 784 - 729 = 0
2х² - 56х + 55 = 0
56х - 2х² = 55
2 * х (28 -х) = 55  
х * (28 - х) = 27,5 - это и есть площадь прямоугольника, т.к. 
х - ширина  
(28 - х) - длина

Ответ: 27,5
 

Answer 2

Solution:

Given: - Diagonal of the rectangle, d = 27 - Perimeter of the rectangle, P = 56

We can use the following formulas to find the area of the rectangle:

1. Area of a rectangle using diagonal and perimeter: - If d is the diagonal and P is the perimeter, then the area A can be calculated using the formula: \[ A = \frac{d}{2} \times \sqrt{\left(\frac{P}{2}\right)^2 - \left(\frac{d}{2}\right)^2} \]

Let's substitute the given values into the formula to find the area.

Using the given values: - \( d = 27 \) - \( P = 56 \)

We can calculate the area using the formula: \[ A = \frac{27}{2} \times \sqrt{\left(\frac{56}{2}\right)^2 - \left(\frac{27}{2}\right)^2} \]

Calculating the values: \[ A = \frac{27}{2} \times \sqrt{784 - 364.5} \] \[ A = \frac{27}{2} \times \sqrt{419.5} \] \[ A \approx \frac{27}{2} \times 20.47 \] \[ A \approx 10.235 \times 20.47 \] \[ A \approx 209.53 \]

Answer:

The area of the rectangle is approximately 209.53 square units.