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

The perimeter of a triangle is the distance around the outside, and can be found by adding the side lengths together: .

The first point of business is to realize is that we have a 45-45-90 triangle. That means the two legs of our triangle are congruent and are thus each 8. We can find our hypotenuse by multiplying by . Thus our hypotenuse is .

Our perimeter is simply the sum of of the lengths of our three sides.

We are given that is a triangle and that . Calculate the length of sides and using either the Pythagorean Theorem or the ratio of the sides of a triangle.

Using the Pythagorean Theorem:

Because is a triangle, we know so we can represent both legs of the triangle with one variable. Let's use .

Using the ratio of the sides:

Divide the length of the hypotenuse by .

Either way, the length of

Calculate the perimeter by adding the length of all the sides.

This can be factored to .

The problem tells us the triangle is 45/45/90. The goal is to solve for the perimeter, which can be determined through , where the s's are in reference to the three sides and P stands for perimeter.

In the figure, two of the three sides are given. In order to calculate the hypotenuse, two methods are possible:

1. using the Pythagorean Theorem

2. using

After calculations, the hypotenuse is

Perimeter can be calculated out to be:

In order to solve for the perimter (the sum of all sides), all side lengths must be known.

Because it's been stated the triangle is 45/45/90, this means that it is also isosceles. Therefore, given that one of the leg lengths is 5 cm, this means that the other leg must also be 5 cm. This leaves the hypotenuse as unknown; let's label this as x.

The third side can be easily determined through the Pythagorean Theorem because it's a right triangle.

, c=x

But because the hypotenuse measures distance, x cannot be a negative number. Therefore, x=5√2.

Now, perimeter can be solved for.

To find the perimeter we must find the hypotenuse and then sum all side lengths to find the perimeter. Remember the hypostenuse of an isoceles right triangle is the side length multiplied by the square root of .

Thus,

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.