Question

в прямоугольном треугольнике АВС к гипотенузе АВ проведена высота СD, ВС=6 см, BD=3см. Найти гипотенузу АВ.

Answer 1

По теореме о высоте, проведенной из вершины прямого угла в прямоугольном треугольнике имеем:

BC^2=BD*AB,

ab=BC^2/BD=36/3=12

Ответ. АВ=12 см.

 

Answer 2

Finding the length of the hypotenuse AB in a right triangle ABC

To find the length of the hypotenuse AB in a right triangle ABC, 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 this case, the hypotenuse AB is given, and a perpendicular CD is drawn from the vertex C to the hypotenuse AB. The length of BC is given as 6 cm, and BD is given as 3 cm.

Let's denote the length of AB as x. According to the Pythagorean theorem, we have the equation:

x^2 = BC^2 + BD^2

Substituting the given values, we get:

x^2 = 6^2 + 3^2

Simplifying the equation:

x^2 = 36 + 9 x^2 = 45

Taking the square root of both sides, we find:

x = √45

Simplifying the square root:

x = √(9 * 5) x = √9 * √5 x = 3√5

Therefore, the length of the hypotenuse AB is 3√5 cm.