match each triangle description to its correct missing side length. use the pythagorean theorem. answer choices: 13, √24, √21, 25, 21, 24, √170, 170, 21, 15. drag the answer choices to the correct category over here! a triangle has legs of 9 units and 12 units. what is the hypotenuse? a triangle has a hypotenuse of 29 units and one leg of 20 units. what is the missing leg? a triangle has legs of 7 units and 11 units. what is the hypotenuse? a triangle has one leg of 10 units and a hypotenuse of 26 units. what is the missing leg?

Question

Accepted Answer

# Explanation:
## Step1: Apply Pythagorean theorem for first triangle
The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 9$, $b = 12$.
$$
\begin{align*}
c^{2}&=9^{2}+12^{2}\
c^{2}&=81 + 144\
c^{2}&=225\
c&=\sqrt{225}=15
\end{align*}
$$
## Step2: Apply Pythagorean theorem for second triangle
Here $c = 29$, $a = 20$.
$$
\begin{align*}
b^{2}&=c^{2}-a^{2}\
b^{2}&=29^{2}-20^{2}\
b^{2}&=841-400\
b^{2}&=441\
b&=\sqrt{441}=21
\end{align*}
$$
## Step3: Apply Pythagorean theorem for third triangle
Here $a = 7$, $b = 11$.
$$
\begin{align*}
c^{2}&=7^{2}+11^{2}\
c^{2}&=49+121\
c^{2}&=170\
c&=\sqrt{170}
\end{align*}
$$
## Step4: Apply Pythagorean theorem for fourth triangle
Here $c = 26$, $a = 10$.
$$
\begin{align*}
b^{2}&=c^{2}-a^{2}\
b^{2}&=26^{2}-10^{2}\
b^{2}&=676 - 100\
b^{2}&=576\
b&=\sqrt{576}=24
\end{align*}
$$

# Answer:
A triangle has legs of 9 units and 12 units: $15$; A triangle has a hypotenuse of 29 units and one leg of 20 units: $21$; A triangle has legs of 7 units and 11 units: $\sqrt{170}$; A triangle has one leg of 10 units and a hypotenuse of 26 units: $24$

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QUESTION IMAGE

Question

Explanation:

Step1: Apply Pythagorean theorem for first triangle

Step2: Apply Pythagorean theorem for second triangle

Step3: Apply Pythagorean theorem for third triangle

Step4: Apply Pythagorean theorem for fourth triangle

Answer: