Question

Знайдіть сторони прямокутника, діагональ якого дорівнює 10 м, а площа-48м.кв

Answer 1

Проведем диагональ, она разбивает прямоугольник на 2 прямоугольных треугольника, диагональ прямоугольника является гипотенузой треугольника =10 , по теореме Пифагора мы находим что стороны равны 6 и 8 

Answer 2

Finding the Sides of a Rectangle with a Diagonal of 10m and an Area of 48m²

To find the sides of a rectangle with a diagonal of 10m and an area of 48m², we can use the following steps:

1. Let's assume the length of the rectangle is L and the width is W. 2. We know that the diagonal of a rectangle divides it into two right triangles. The length of the diagonal can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. 3. In this case, the diagonal is 10m, so we have the equation: L² + W² = 10². 4. We also know that the area of a rectangle is equal to the product of its length and width. In this case, the area is 48m², so we have the equation: L * W = 48.

Now, let's solve these equations to find the sides of the rectangle.

From equation 2, we can express L in terms of W: L = 48 / W.

Substituting this value of L into equation 1, we get: (48 / W)² + W² = 100.

Simplifying this equation, we have: 2304 + W⁴ - 100W² = 0.

To solve this equation, we can use numerical methods or approximate solutions. However, since the equation is quite complex, it may be difficult to find an exact solution.

Alternatively, we can use trial and error to find approximate values for W that satisfy the equation. Let's try some values:

- If we assume W = 4, then L = 48 / 4 = 12. Checking the equation, we have: 12² + 4² = 160, which is not equal to 100. - If we assume W = 6, then L = 48 / 6 = 8. Checking the equation, we have: 8² + 6² = 100, which is equal to 100.

Therefore, the sides of the rectangle are approximately 8m and 6m.

Please note that these values are approximate and may not be exact due to the complexity of the equation.