Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=8\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=8+8+8\sqrt2=27.31$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=9\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=9+9+9\sqrt2=30.73$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=11\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=11+11+11\sqrt2=37.56$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=14\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=14+14+14\sqrt2=47.80$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=20\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=20+20+20\sqrt2=68.28$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=19\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=19+19+19\sqrt2=64.87$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=16\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=16+16+16\sqrt2=54.63$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=4\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=22+22+22\sqrt2=75.11$

Recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+b+c$

Now, because this is a right isosceles triangle, we know the following:

$\displaystyle a=b$

From the information given in the question, we already have two of the sides needed. Now, recall the Pythagorean Theorem to find the third side of the triangle, the hypotenuse.

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

The Pythagorean Theorem can then be simplifed to the following equation:

$\displaystyle a^2+a^2=2a^2=c^2$

Now, solve for $\displaystyle c$ since the question asks for the length of the hypotenuse.

$\displaystyle c=\sqrt{2a^2}$

$\displaystyle c=a\sqrt2$

Now, plug in the given value for $\displaystyle a$ to find the length of the hypotenuse.

$\displaystyle c=13\sqrt2$

Now that we have all three sides of the triangle, we can find the perimeter. Use a calculator and round to $\displaystyle 2$ decimal places.

$\displaystyle \text{Perimeter}=13+13+13\sqrt2=44.38$

Notice that the given triangle is a right isosceles triangle. The two legs with the tick marks are the same length.

The lengths of the legs in the given triangle are then $\displaystyle 12$.

Next, find the length of the hypotenuse by using the Pythagorean Theorem.

$\displaystyle a^2+a^2=b^2$

$\displaystyle b^2=2a^2$

$\displaystyle b=a\sqrt2$

Plug in the value of the length of a leg to find the length of the hypotenuse.

$\displaystyle b=12\sqrt2$

Finally, recall how to find the perimeter of a triangle:

$\displaystyle \text{Perimeter}=a+a+b$

Plug in the values for this triangle to find its perimeter.

$\displaystyle \text{Perimeter}=12+12+12\sqrt2=40.97$

Make sure to round to two places after the decimal.