Одна из сторон прямоугольника больше другой на 7 см , а его диаганаль равна 13 см . найдите стороны прямоугольника

Let's assume that the shorter side of the rectangle has a length of 'x' cm.

According to the given information, the longer side will then have a length of 'x + 7' cm.

We can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have:

(x)^2 + (x + 7)^2 = 13^2

Expanding and simplifying the equation:

x^2 + x^2 + 14x + 49 = 169

Combining like terms:

2x^2 + 14x + 49 = 169

Rearranging the equation:

2x^2 + 14x - 120 = 0

Now, we can solve this quadratic equation for 'x' using factoring or the quadratic formula.

By factoring:

2x^2 + 14x - 120 = 0 2(x^2 + 7x - 60) = 0 2(x + 12)(x - 5) = 0

Setting each factor equal to zero:

x + 12 = 0 or x - 5 = 0

Solving for 'x':

x = -12 (discarding as length cannot be negative) or x = 5

So, the shorter side of the rectangle is 5 cm and the longer side is 5 + 7 = 12 cm.