3 multiple choice 4 points what is the length of $ \overline{yz} $? 9 cm 19 cm 25 cm 15 cm 4 multiple choice 4 points what is the length of the missing side of this triangle? 2 $ \sqrt{514} $ 8 $ \sqrt{2} $

Question

Accepted Answer

# Answer:
3. D. 15 cm
4. C. 8

# Explanation:
## Step1: Apply Pythagorean theorem
For a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse.
## Step2: Solve for the first triangle (Question 3)
Let $XY = a = 8$ cm, $XZ=c = 17$ cm, and $YZ = b$.
$$
\begin{align*}
b&=\sqrt{c^{2}-a^{2}}\
&=\sqrt{17^{2}-8^{2}}\
&=\sqrt{(17 + 8)(17 - 8)}\
&=\sqrt{25\times9}\
&=\sqrt{225}\
& = 15
\end{align*}
$$
## Step3: Solve for the second triangle (Question 4)
Let the missing side be $a$, $b = 15$, $c = 17$.
$$
\begin{align*}
a&=\sqrt{c^{2}-b^{2}}\
&=\sqrt{17^{2}-15^{2}}\
&=\sqrt{(17 + 15)(17 - 15)}\
&=\sqrt{32\times2}\
&=\sqrt{64}\
&=8
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Apply Pythagorean theorem

Step2: Solve for the first triangle (Question 3)

Step3: Solve for the second triangle (Question 4)

Answer: