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)

Question

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.