Question

to solve for the lengths of the right triangle sides, which equation is correct? a. x^2+(3x - 1)^2=(5x + 7)^2 b. x^2+(5x + 7)^2=(3x - 1)^2 c. x^2=(3x - 1)^2-(5x + 7)^2 d. x^2=(3x - 1)^2+(5x + 7)^2 to solve for the lengths of the right triangle sides, equation (type a, b, c, or d.) is correct.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse.

Step2: Identify sides in the triangle

In the given right - triangle, the sides are $x$, $3x - 1$ and the hypotenuse is $5x+7$ (longest side).

Step3: Apply Pythagorean theorem

Substitute $a = x$, $b=3x - 1$ and $c = 5x + 7$ into $a^{2}+b^{2}=c^{2}$, we get $x^{2}+(3x - 1)^{2}=(5x + 7)^{2}$.

Answer:

A. $x^{2}+(3x - 1)^{2}=(5x + 7)^{2}$