Question

В треугольнике авс угол с равен 90 градусов ас=вс=14см. две стороны квадрата сдеф лежат на катетах треугольника авс а вершина е принадлежит гипотенузе ав. найдите периметр квадрата сдеф?

Answer 1

14*4=56 т.к у квадрата все стороны равны в данном примере стороны у нас ас и бс которые равны 14см

Answer 2

Problem Analysis

We are given a right triangle ABC, where angle C is 90 degrees and AC = BC = 14 cm. We are also given that two sides of the square SDEF lie on the legs of the triangle ABC, and vertex E lies on the hypotenuse AB. We need to find the perimeter of the square SDEF.

Solution

To find the perimeter of the square SDEF, we need to find the length of one side of the square and then multiply it by 4.

Let's start by finding the length of the hypotenuse AB using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In triangle ABC, AC = BC = 14 cm, and angle C is 90 degrees. Using the Pythagorean theorem, we can find the length of AB as follows:

AB^2 = AC^2 + BC^2 Substituting the given values:

AB^2 = 14^2 + 14^2

Simplifying:

AB^2 = 196 + 196

AB^2 = 392

Taking the square root of both sides:

AB = sqrt(392)

Using a calculator, we find that AB ≈ 19.8 cm.

Now, let's find the length of one side of the square SDEF. Since two sides of the square lie on the legs of the triangle ABC, and vertex E lies on the hypotenuse AB, we can conclude that the length of one side of the square is equal to the length of the altitude from vertex E to the hypotenuse AB.

To find the length of this altitude, we can use the formula for the altitude of a right triangle, which states that the altitude squared is equal to the product of the two segments of the hypotenuse.

In triangle ABC, let's denote the length of the altitude from vertex E to the hypotenuse AB as h. Using the altitude formula, we have:

h^2 = AC * BC Substituting the given values:

h^2 = 14 * 14

h^2 = 196

Taking the square root of both sides:

h = sqrt(196)

Using a calculator, we find that h = 14 cm.

Therefore, the length of one side of the square SDEF is 14 cm.

Finally, we can find the perimeter of the square SDEF by multiplying the length of one side by 4:

Perimeter of SDEF = 4 * 14 cm = 56 cm.

So, the perimeter of the square SDEF is 56 cm.

Answer

The perimeter of the square SDEF is 56 cm.