Question

find x.
10 cm
x
8 cm
x = centimeters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, the hypotenuse is 10 cm, one leg is 8 cm and the other leg is $x$. So, $x^{2}+8^{2}=10^{2}$.

Step2: Simplify the equation

$x^{2}+64 = 100$. Then, $x^{2}=100 - 64$.

Step3: Calculate $x^{2}$

$x^{2}=36$.

Step4: Solve for $x$

Taking the square root of both sides, $x=\sqrt{36}$. Since $x$ represents a length, we take the positive square root, so $x = 6$.

Answer:

6