Question

for the right triangle below, find the length of x.
5
13
x =
round to the nearest hundredth (two decimal places).

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse $x$, $a=5$, $b=13$.
$$x^2 = 5^2 + 13^2$$

Step2: Calculate squared terms

Compute the squares of the legs.
$$x^2 = 25 + 169$$

Step3: Sum the squared terms

Add the two values together.
$$x^2 = 194$$

Step4: Solve for x

Take the square root of the sum.
$$x = \sqrt{194}$$

Step5: Round to nearest hundredth

Calculate the decimal value and round to two places.
$$x \approx 13.93$$

Answer:

13.93