What is the perimeter? If necessary, round to the nearest tenth.

Steps to Solve

1. Identify the lengths of the sides We have two sides of the right triangle: one side is $10 \text{ cm}$ (the hypotenuse) and the other is $7 \text{ cm}$ (one leg).

2. Apply the Pythagorean theorem To find the length of the third side ($b$), we use the Pythagorean theorem:

$$ a^2 + b^2 = c^2 $$

Here, $c$ is the hypotenuse ($10 \text{ cm}$), and $a$ is the known leg ($7 \text{ cm}$). So we rearrange the equation to find $b$:

$$ b = \sqrt{c^2 - a^2} $$

3. Substitute the known values Substituting the known values into the equation:

$$ b = \sqrt{10^2 - 7^2} $$

Calculating gives:

$$ b = \sqrt{100 - 49} = \sqrt{51} $$

4. Calculate the value of b Now, we compute the square root:

$$ b \approx 7.1 \text{ cm} $$

5. Calculate the perimeter Now that we have all three sides, we can find the perimeter ($P$):

$$ P = a + b + c = 7 \text{ cm} + 7.1 \text{ cm} + 10 \text{ cm} $$

Calculating this gives:

$$ P \approx 24.1 \text{ cm} $$