Question

ОЧЕНЬ СРОЧНО!!! РЕБЯТА, ПОМОГИТЕ!!!!!! 8 КЛАСС Найдите боковую сторону равнобокой трапеции, осования которой равны 7 см и 25 см, а диагонали перпендикулярны боковым сторонам.

Answer 1

Решение смотри на фото

Answer 2

Finding the Side Length of an Isosceles Trapezoid

To find the side length of an isosceles trapezoid, we need to use the given information about the bases and perpendicular diagonals.

Let's denote the bases of the trapezoid as a and b, and the perpendicular diagonals as c and d.

From the given information, we have: - Base a = 7 cm - Base b = 25 cm - Perpendicular diagonals are perpendicular to the side lengths.

To find the side length of the trapezoid, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In our case, we can consider the trapezoid as a right trapezoid, where the perpendicular diagonals act as the hypotenuses of the right triangles formed.

Let's label the side length we want to find as x.

Using the Pythagorean theorem, we can set up the following equations:

For the right triangle formed by base a, side length x, and diagonal c: x^2 + (0.5(a - b))^2 = c^2 For the right triangle formed by base b, side length x, and diagonal d: x^2 + (0.5(a + b))^2 = d^2 By substituting the given values into these equations, we can solve for x.

Let's calculate the value of x using the given information:

Substituting the given values: x^2 + (0.5(7 - 25))^2 = c^2 x^2 + (-9)^2 = c^2 x^2 + 81 = c^2 Equation 1

x^2 + (0.5(7 + 25))^2 = d^2 x^2 + (16)^2 = d^2 x^2 + 256 = d^2 Equation 2

To find the value of x, we need to solve Equations 1 and 2 simultaneously.

By subtracting Equation 1 from Equation 2, we get: d^2 - c^2 = 256 - 81 (d + c)(d - c) = 175

Since the diagonals are perpendicular to the side lengths, we can assume that d + c = b and d - c = a.

Substituting these values into the equation: b * a = 175

Substituting the given values: 25 * 7 = 175

Therefore, the product of the bases is equal to 175.

Now, we can solve for x by dividing the product of the bases by the sum of the bases: x = (b * a) / (b + a) x = (25 * 7) / (25 + 7) x = 175 / 32 x ≈ 5.47 cm

Therefore, the side length of the isosceles trapezoid is approximately 5.47 cm.

Please note that the calculations provided are based on the given information and assumptions made about the trapezoid.