How to find the height of an isosceles triangle

All Intermediate Geometry Resources

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All Intermediate Geometry Resources
All Intermediate Geometry Resources
How do I find the height of a triangle?
What is the formula for finding an isosceles triangle?
How do you find the height of an isosceles triangle using Pythagoras?

An isosceles triangle has a base of and an area of

. What must be the height of this triangle?

Correct answer:

An isosceles triangle has a perimeter of . If the base of the triangle is two less than two times the length of each leg, what is the height of the triangle?

Possible Answers:

The height of the triangle cannot be determined with the given information.

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.

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.

An isosceles triangle has a perimeter of . If the base of the triangle is less than three times the length of a leg, what is the height of the triangle?

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.

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.

An isosceles triangle has a perimeter of . If the length of the base is one less than twice the length of a leg, what is the height of the triangle?

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.

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.

An isosceles triangle has a perimeter of . If the length of the base is fourteen less than three times the length of a leg, what is the height of the triangle?

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.

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.

An isosceles triangle has a perimeter of . If the length of the base is two less than one-third of the length of a leg, what is the height of the triangle?

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.

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.

An isosceles triangle has a perimeter of . If the length of the base is ten less than twice the length of a leg, what is the height of the triangle?

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

All Intermediate Geometry Resources

How do I find the height of a triangle?

Given triangle area The well-known equation for the area of a triangle may be transformed into a formula for the altitude of a right triangle: area = b × h / 2 , where b is a base, h - height. so h = 2 × area / b.

What is the formula for finding an isosceles triangle?

Various formulas for isosceles triangles are explained below..

Area = 1/2 × Base × Height..

Area = b2√a2−b24. (Here a is the equal side, and b is the base of the triangle.).

Area = 1/2 ×abSinα (Here a and b are the lengths of two sides and α is the angle between these sides.).

How do you find the height of an isosceles triangle using Pythagoras?

We can find the height by splitting the isosceles triangle into two right-angled triangles and then applying Pythagoras' Theorem to one of them. h = 13.20 ( t o 2 d . p . ) We now know the height of the triangle and can use this to go back and find the area of the isosceles triangle.