os lados de um triângulo abc medem 26 cm, 24 cm e x cm. sabendo que esse triângulo é retângulo e que a hipotenusa mede 26 cm, qual o valor da medida x?
What is the value of x in the triangle ABC with sides measuring 26 cm, 24 cm, and x cm, knowing that the triangle is a right-angled triangle and the hypotenuse measures 26 cm?
Answer:
In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This relationship is represented by the Pythagorean theorem: a² + b² = c², where a and b are the lengths of the two shorter sides (legs) of the right triangle, and c is the length of the hypotenuse.
Given that the sides of triangle ABC are 26 cm, 24 cm, and x cm, and the hypotenuse is 26 cm, we can set up the equation:
26² = 24² + x²
Solving this equation will help find the value of x:
676 = 576 + x²
100 = x²
x = 10
Therefore, the value of x in the triangle ABC is 10 cm.