Question

A right triangle has legs of lengths x and 2x12 and a hypotenuse of length 2x13. what are the lengths of its sides?

Answer 1

Step-by-step explanation:

In a right triangle, the Pythagorean theorem holds, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

\[c^2 = a^2 + b^2\]

In this case:

\[ (2x^{13})^2 = x^2 + (2x + 12)^2 \]

Solving this equation will give you the values for \(x\) and then you can find the lengths of the sides using those values.

Answer 2

The Pythagorean theorem is used to find the lengths of the sides of a right triangle, with the legs expressed as x and 2x + 12, and the hypotenuse as 2x + 13. Solve x² + (2x + 12)² = (2x + 13)² to find the value of x.

Step-by-step explanation:

The subject of the question is to find the lengths of the sides of a right triangle given certain expressions for their lengths. According to the Pythagorean theorem which relates the lengths of the legs of a right triangle with the hypotenuse, the equation is a² + b² = c².

In this situation, the legs are given as x and 2x + 12, and the hypotenuse is given as 2x + 13. Plugging these values into the theorem, we get:

• x² + (2x + 12)² = (2x + 13)²

By solving this equation, we can find the value of x and thus determine the exact lengths of the triangle's legs.