What is the value of x if $$\frac{3}{x} = \frac{x}{4}$$ ?

Cross-multiplying gives: $$3 \times 4 = x^2$$ , thus $$x^2 = 12$$ , so $$x = 2\text{√}3$$ .

What is the formula for the area of a right triangle?

The area of a right triangle can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

If the lengths of the sides of a triangle are 5, 12, and 13, does it form a right triangle?

Yes, because $$5^2 + 12^2 = 25 + 144 = 169 = 13^2$$ .

What is the geometric mean of 4 and 16?

The geometric mean is calculated as: $$\text{Geometric Mean} = \text{√}(4 \times 16) = \text{√}(64) = 8$$ .

What is the value of b if the altitude of a triangle is $$6\text{√}3$$ ?

If the altitude is $$6\text{√}3$$ , then the area can be calculated using the base and height.

What is the significance of the hypotenuse in a right triangle?

The hypotenuse is the longest side of a right triangle and is opposite the right angle.

How do you find the length of a missing side in a right triangle?

Use the Pythagorean Theorem: if you know two sides, you can find the third side using $$c^2 = a^2 + b^2$$ .

What is the relationship between the geometric mean and the Pythagorean theorem?

The geometric mean can be used in right triangles to find the altitude to the hypotenuse, which relates to the Pythagorean theorem.

What is the value of x if $$\frac{a}{x} = \frac{x}{b}$$ ?

Cross-multiplying gives: $$a \times b = x^2$$ , thus $$x = \text{√}(a \times b)$$ .

Pythagorean Theorem & Geometric Mean

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

8.G.B.8, 6.G.A.1, 8.G.B.7

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

Tags

CCSS.8.G.B.8

FLASHCARD QUESTION

Front

What is the formula for the geometric mean of two numbers a and b?

Back

FLASHCARD QUESTION

Front

If a right triangle has legs of length 3 and 4, what is the length of the hypotenuse?

Back

Tags

CCSS.8.G.B.7

FLASHCARD QUESTION

Front

What is the relationship between the sides of a right triangle?

Back

Tags

CCSS.8.G.B.8

FLASHCARD QUESTION

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Tags

CCSS.8.G.B.8

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

FLASHCARD QUESTION

Front

What is the altitude of a triangle with a base of 8 and an area of 24?

Back

Tags

CCSS.6.G.A.1

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