Question

Діагональ прямокутника на 8 см більша за одну з його сторін. Знайти сторони прямокутника.​

Answer 1

По теореме Пифагора х² = (х-8) ² + (х-4) ².

х²=х²-16 х+64+х²-8 х+16.

х²-24 х+80=0

х=20, х=4 - этот корень не подходит: по условию задачи корень должен быть больше 8.

20 см - диагональ, стороны 12 и 16 см.

Answer 2

Finding the Sides of the Rectangle

To find the sides of the rectangle when the diagonal is 8 cm longer than one of its sides, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 lengths of the other two sides.

Let's denote the sides of the rectangle as x and x + 8 (since the diagonal is 8 cm longer than one of its sides).

Using the Pythagorean theorem, we have:

x^2 + (x + 8)^2 = diagonal^2

Now, we can solve for x to find the sides of the rectangle.