# Basic Geometry : How to find the perimeter of a 45/45/90 right isosceles triangle

## Example Questions

### Example Question #11 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #12 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #13 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #14 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #15 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #16 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #17 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #18 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #19 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

What is the perimeter of a right isosceles triangle with leg lengths of ?

Explanation:

Recall how to find the perimeter of a triangle:

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

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.

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

Now, solve for  since the question asks for the length of the hypotenuse.

Now, plug in the given value for  to find the length of the hypotenuse.

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

### Example Question #20 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Find the perimeter.

Explanation:

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 .

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

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

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

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

Make sure to round to two places after the decimal.