High School Math : How to find the perimeter of a 45/45/90 right isosceles triangle

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Isosceles

The hypotenuse of an isosceles right triangle has a measure of . Find its perimeter.

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

In order to calculate the triangle's perimeter, we need to find the lengths of its legs.  An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as  triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

Now we can calculate the perimeter by doubling  and adding .

Example Question #2 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

Isosceles

The side lengths of an isoceles right triangle measure . Find its perimeter.

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

An isosceles triangle is a special triangle due to the values of its angles.  These triangles are referred to as  triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.

Now we can calculate the perimeter by doubling  and adding .

Example Question #1 : How To Find The Perimeter Of A 45/45/90 Right Isosceles Triangle

A triangle has two angles equal to and two sides equal to . What is the perimeter of this triangle?

Possible Answers:

Correct answer:

Explanation:

When a triangle has two angles equal to , it must be a isosceles right triangle.

The pattern for the sides of a is .

Since two sides are equal to , this triangle will have sides of .

Add them all together to get .

Example Question #442 : Psat Mathematics

An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?

Possible Answers:

None of these

Correct answer:

Explanation:

An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).

The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).

5 + 5 + 6 = 16

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