Question

Question
A 45-45-90 triangle has a leg that is 5 cm long. Find the perimeter of the triangle to the nearest tenth.(1 point)
The perimeter is
cm.

Answer 1

In a 45-45-90 triangle, the legs are of equal length, and the lengths of the sides are in the ratio 1 : 1 : √2. Since both legs are 5 cm, we can find the length of the hypotenuse using the formula:

\[
\text{Hypotenuse} = \text{leg} \times \sqrt{2} = 5 \times \sqrt{2}
\]

Calculating the hypotenuse:

\[
5 \times \sqrt{2} \approx 5 \times 1.414 \approx 7.07 \text{ cm}
\]

Now, we can find the perimeter of the triangle by adding the lengths of all sides:

\[
\text{Perimeter} = \text{leg} + \text{leg} + \text{hypotenuse} = 5 + 5 + 7.07 = 17.07 \text{ cm}
\]

Rounding to the nearest tenth:

\[
\text{Perimeter} \approx 17.1 \text{ cm}
\]

Thus, the perimeter of the triangle is approximately **17.1 cm**.