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 equal and the lengths of the legs can be represented as \( x \). The length of the leg is given as 5 cm.

To find the length of the hypotenuse \( c \) in a 45-45-90 triangle, we use the formula:

\[
c = x\sqrt{2}
\]

Substituting the length of the leg:

\[
c = 5\sqrt{2}
\]

Now we can calculate \( 5\sqrt{2} \):

\[
5\sqrt{2} \approx 5 \times 1.4142 \approx 7.071
\]

Next, we can find the perimeter \( P \) of the triangle, which is the sum of all sides:

\[
P = \text{leg} + \text{leg} + \text{hypotenuse} = 5 + 5 + 5\sqrt{2}
\]

Substituting the value we calculated for the hypotenuse:

\[
P = 5 + 5 + 7.071 \approx 10 + 7.071 = 17.071
\]

Rounding to the nearest tenth:

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

Therefore, the perimeter of the triangle is **17.1 cm**.