Question

В треугольнике АВС высота СД, опущенная из вершины прямого угла С, делит гипотенузу АВ на отрезки АД = 5 см и ДВ = 4 см. Чему равен катет ВС? Пожалуйста помогите решить

Answer 1

Ответ:

6 см.                                  

Объяснение:

Дано: ΔАВС - прямоугольный, СД - высота, АД=5 см, ВД=4 см. Найти ВС.

СД=√(АД*ВД)=√(5*4)=√20 см.

По теореме Пифагора

ВС²=(√20)²+4²=20+16=36;  ВС=√36=6 см.

Answer 2

Problem Analysis

We are given a right triangle ABC, with CD as the altitude dropped from the vertex of the right angle C. The lengths of AD and DV are given as 5 cm and 4 cm, respectively. We need to find the length of side BC.

Solution

To solve this problem, we can use the Pythagorean theorem, which 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 our case, the hypotenuse is side AB, and the other two sides are BC and AC. Let's denote the length of BC as x.

According to the Pythagorean theorem, we have the following equation:

AC^2 + BC^2 = AB^2

Since AC is the altitude dropped from the vertex of the right angle C, it is equal to CD. Therefore, we can rewrite the equation as:

CD^2 + BC^2 = AB^2

We are given the lengths of CD (4 cm) and AD (5 cm). Since AD is the sum of CD and DV, we can write:

AD = CD + DV

Substituting the given values, we have:

5 cm = 4 cm + DV

Simplifying, we find:

DV = 1 cm

Now, we can substitute the values of CD (4 cm) and DV (1 cm) into the equation:

4 cm^2 + BC^2 = AB^2

Since AB is the hypotenuse, it is equal to the square root of the sum of the squares of AD and BD:

AB = √(AD^2 + BD^2)

Substituting the given values, we have:

AB = √(5 cm^2 + x^2)

Now, we can substitute the value of AB into the equation:

4 cm^2 + BC^2 = (5 cm^2 + x^2)

Simplifying, we find:

16 cm^2 + BC^2 = 25 cm^2 + x^2

Rearranging the equation, we have:

BC^2 - x^2 = 25 cm^2 - 16 cm^2

BC^2 - x^2 = 9 cm^2

Since we are looking for the length of BC, we can solve for BC by taking the square root of both sides:

√(BC^2 - x^2) = √(9 cm^2)

BC = √9 cm

Simplifying, we find:

BC = 3 cm

Therefore, the length of side BC is 3 cm.

Answer

The length of side BC is 3 cm.