Question

find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be $c$. For a right triangle, $c^2 = a^2 + b^2$, where $a=3$, $b=4$.

$$\begin{aligned} c^2 &= 3^2 + 4^2 \end{aligned}$$

Step2: Calculate squared terms

Compute the squares of the known sides.

$$\begin{aligned} c^2 &= 9 + 16 \end{aligned}$$

Step3: Sum and solve for $c$

Add the values, then take the square root.

$$\begin{aligned} c^2 &= 25 \\ c &= \sqrt{25} = 5 \end{aligned}$$

Answer:

5