Question

for the following right triangle, find the side length x. right triangle image with legs 9 and 40, hypotenuse x

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Here, $a=9$, $b=40$, $c=x$.
$\boldsymbol{9^2 + 40^2 = x^2}$

Step2: Calculate squared side values

Compute the squares of the known sides.
$\boldsymbol{81 + 1600 = x^2}$

Step3: Sum and solve for x

Add the values, then take the square root.
$\boldsymbol{1681 = x^2}$
$\boldsymbol{x = \sqrt{1681}}$

Answer:

41