Question

find the values of (x) and (y). if your answer cannot be expressed as a rational number, use square root notation to enter the value. the value of (x) is . the value of (y) is .

Explanation:

Step1: Use Pythagorean theorem for $x$

For the right - triangle with legs 5 and 8, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 5$, $b = 8$, and $c=x$. So $x=\sqrt{5^{2}+8^{2}}=\sqrt{25 + 64}=\sqrt{89}$.

Step2: Use Pythagorean theorem for $y$

The base of the large right - triangle is $4 + 8=12$, and the height is 5. By the Pythagorean theorem, $y=\sqrt{5^{2}+(4 + 8)^{2}}=\sqrt{25+144}=\sqrt{169}=13$.

Answer:

The value of $x$ is $\sqrt{89}$.
The value of $y$ is $13$.