Question

find the perimeter and area of the right triangle shown below.
13 cm
10 cm
perimeter = cm
area = cm²
round your answers to the nearest hundredth as needed.

Explanation:

Step1: Solve for missing side $x$

Use Pythagorean theorem: $x = \sqrt{13^2 - 10^2}$

$$\begin{align*} x &= \sqrt{169 - 100} \\ &= \sqrt{69} \\ &\approx 8.31 \end{align*}$$

Step2: Calculate perimeter

Sum all sides: $\text{Perimeter} = x + 10 + 13$

$$\begin{align*} \text{Perimeter} &\approx 8.31 + 10 + 13 \\ &= 31.31 \end{align*}$$

Step3: Calculate area

Use right triangle area formula: $\text{Area} = \frac{1}{2} \times 10 \times x$

$$\begin{align*} \text{Area} &\approx \frac{1}{2} \times 10 \times 8.31 \\ &= 41.55 \end{align*}$$

Answer:

Perimeter = 31.31 cm
Area = 41.55 $\text{cm}^2$