Question

Гипотенуза равнобедренного прямоугольного треугольника равна 8 см. найдите его катеты

Answer 1

Пусть катеты равны х, по теореме пифагора x^2+x^2=8^2=64
2x^2=64
x^2=32
x=√32=√16*2=4√2

Answer 2

Solution for Finding the Catheti of an Isosceles Right-Angled Triangle

To find the catheti of an isosceles right-angled triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the given hypotenuse length of 8 cm, we can calculate the lengths of the catheti as follows:

Step 1: Apply the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the lengths of the catheti and \( c \) is the length of the hypotenuse.

Step 2: Substitute the given hypotenuse length: \( a^2 + b^2 = 8^2 = 64 \).

Step 3: Solve for the catheti: - \( a^2 + b^2 = 64 \) - \( a^2 = 64 - b^2 \) - \( a = \sqrt{64 - b^2} \)

Step 4: Substitute the value of \( a \) into the equation to solve for \( b \).

Step 5: Calculate the value of \( b \) using the equation.

Step 6: Calculate the value of \( a \) using the equation.

Based on the Pythagorean theorem, the lengths of the catheti of the isosceles right-angled triangle are \( a = 4\sqrt{2} \) cm and \( b = 4\sqrt{2} \) cm.

Therefore, the lengths of the catheti of the given isosceles right-angled triangle are both 4√2 cm.