Question

for the following right triangle, find the side length x.
right triangle image with legs 6 and 8, hypotenuse x

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Here, $a=6$, $b=8$, $c=x$.
$$6^2 + 8^2 = x^2$$

Step2: Calculate squared side values

Compute the squares of the known sides.
$$36 + 64 = x^2$$

Step3: Sum and solve for x

Add the values, then take the square root.
$$100 = x^2 \implies x = \sqrt{100}$$

Answer:

10