Intermediate Geometry : How to find the height of of an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

2 Next →

Example Question #11 : Triangles

The perimeter of an isosceles triangle is . If the length of the base is eleven less than twice the length of a leg, what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

First, find the lengths of the triangle.

Let  be the length of each leg. Then, the length of the base must be .

Use the information given about the perimeter to solve for .

Plug this value in to find the length of the base.

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

13

Thus, we can use the Pythagorean Theorem to find the length of the height.

Plug in the given values to find the height of the triangle.

Make sure to round to  places after the decimal.

 

Example Question #12 : Triangles

The perimeter of an isosceles triangle is . If the length of the base is fifteen more than one-third the length of a leg, what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

First, find the lengths of the triangle.

Let  be the length of each leg. Then, the length of the base must be .

Use the information given about the perimeter to solve for .

Plug this value in to find the length of the base.

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

13

Thus, we can use the Pythagorean Theorem to find the length of the height.

Plug in the given values to find the height of the triangle.

Make sure to round to  places after the decimal.

 

Example Question #13 : Triangles

An isosceles triangle has a perimeter of . If the length of the base is seven more than one-seventh of the length of a leg, what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

First, find the lengths of the triangle.

Let  be the length of each leg. Then, the length of the base must be .

Use the information given about the perimeter to solve for .

Plug this value in to find the length of the base.

Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.

13

Thus, we can use the Pythagorean Theorem to find the length of the height.

Plug in the given values to find the height of the triangle.

Make sure to round to  places after the decimal.

 

2 Next →
Learning Tools by Varsity Tutors