Calculate Pyramid Height: 150m Sides and 120m Base Using Geometry

Q: Why do I divide the base by 2?

The height of an isosceles triangle always bisects the base, creating two identical right triangles. Each right triangle has a base of half the original base length (60m, not 120m).

Q: How do I simplify √18900?

Factor out perfect squares: $ \sqrt{18900} = \sqrt{900 \times 21} = \sqrt{900} \times \sqrt{21} = 30\sqrt{21} $. Look for the largest perfect square factor!

Q: Can I use decimals instead of the radical form?

Yes, but exact answers are preferred in geometry. $ 30\sqrt{21} $ is exact, while 137.48... is an approximation that loses precision.

Q: What if the pyramid isn't isosceles?

This method only works for isosceles triangles where both sides are equal (150m each). For other triangles, you'd need different information like angles or area.

Q: How do I know which leg is which in the Pythagorean theorem?

The hypotenuse (longest side) is always the slant height (150m). The two legs are the height (unknown) and half the base (60m).

Pythagorean Theorem with Isosceles Triangles

The Egyptians decided to build another pyramid that looks like an isosceles triangle when viewed from the side.

Each side of the pyramid measures 150 m, while the base measures 120 m.

What is the height of the pyramid?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What is the height of the pyramid?

00:03 In an isosceles triangle, the height is also a median

00:06 Let's mark half the side length as X

00:10 Let's substitute the side value according to the given data and solve

00:16 We'll use the Pythagorean theorem to find height H

00:22 Let's substitute the value of X

00:26 Let's isolate height H

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The Egyptians decided to build another pyramid that looks like an isosceles triangle when viewed from the side.

Each side of the pyramid measures 150 m, while the base measures 120 m.

What is the height of the pyramid?

Step-by-step solution

Since the height divides the base into two equal parts, each part will be called X

We begin by calculating X: $120:2=60$

We then are able to calculate the height of the pyramid using the Pythagorean theorem:

$X^2+H^2=150^2$

We insert the corresponding data:

$60^2+h^2=150^2$

Finally we extract the root: $h=\sqrt{150^2-60^2}=\sqrt{22500-3600}=\sqrt{18900}$

$h=30\sqrt{21}$

Final Answer

$30\sqrt{21}$ m

Key Points to Remember

Essential concepts to master this topic

Rule: Height bisects the base creating two equal right triangles
Technique: Use $a^2 + h^2 = c^2$ where a = 60, c = 150
Check: Verify $60^2 + (30\sqrt{21})^2 = 150^2$ equals 22500 ✓

Common Mistakes

Avoid these frequent errors

Using the full base length in Pythagorean theorem
Don't use 120 as one leg in the equation = wrong triangle! The height creates two right triangles, each with base 60m (half of 120m). Always divide the base by 2 first to get the correct leg length.

Practice Quiz

Test your knowledge with interactive questions

Consider a right-angled triangle, AB = 8 cm and AC = 6 cm.
Calculate the length of side BC.

FAQ

Everything you need to know about this question

Why do I divide the base by 2?

The height of an isosceles triangle always bisects the base, creating two identical right triangles. Each right triangle has a base of half the original base length (60m, not 120m).

How do I simplify √18900?

Factor out perfect squares: $\sqrt{18900} = \sqrt{900 \times 21} = \sqrt{900} \times \sqrt{21} = 30\sqrt{21}$ . Look for the largest perfect square factor!

Can I use decimals instead of the radical form?

Yes, but exact answers are preferred in geometry. $30\sqrt{21}$ is exact, while 137.48... is an approximation that loses precision.

What if the pyramid isn't isosceles?

This method only works for isosceles triangles where both sides are equal (150m each). For other triangles, you'd need different information like angles or area.

How do I know which leg is which in the Pythagorean theorem?

The hypotenuse (longest side) is always the slant height (150m). The two legs are the height (unknown) and half the base (60m).

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Calculate Pyramid Height: 150m Sides and 120m Base Using Geometry

Pythagorean Theorem with Isosceles Triangles

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I divide the base by 2?

How do I simplify √18900?

Can I use decimals instead of the radical form?

What if the pyramid isn't isosceles?

How do I know which leg is which in the Pythagorean theorem?

🌟 Unlock Your Math Potential

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