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Question

Grant Watson

07/24/2024 · Senior High School

# find the (CD) in the diagram

Patel Schmidt
Qualified Tutor

10

## Solution

UpStudy Free Solution:

To find the length of $$CD$$ in the given diagram, we can use the Pythagorean theorem. The diagram shows a right triangle with $$CB$$ as the base, $$BD$$ as the height, and $$CD$$ as the hypotenuse.

Given:

$CB = 8 \space \text { cm}$

$BD = 6 \space \text { cm}$

The Pythagorean theorem states:

$CD^ 2 = CB^ 2 + BD^ 2$

Substitute the given values:

$CD^ 2 = 8^ 2 + 6^ 2$

$CD^ 2 = 64 + 36$

$CD^ 2 = 100$

Taking the square root of both sides:

$CD = \sqrt { 100}$

$CD = 10 \space \text { cm}$

Therefore, the length of $$CD$$ is $$10 \space \text { cm}$$.

Supplemental Knowledge

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that in a right-angled triangle, the square of the length of the hypotenuse ($$c$$) is equal to the sum of the squares of the lengths of the other two sides ($$a$$ and $$b$$).

Key Concepts:

1. Pythagorean Theorem Formula:

$c^ 2 = a^ 2 + b^ 2$

$$c$$ is the length of the hypotenuse.

$$a$$ and $$b$$ are the lengths of the other two sides.

2. Application Steps:

- Identify which side is the hypotenuse (the side opposite the right angle).

- Square the lengths of both legs.

- Take the square root of this sum to find the length of the hypotenuse.

Consider another right triangle with legs measuring 9 cm and 12 cm. To find the hypotenuse ($$c$$):

$c^ 2 = 9^ 2 + 12^ 2$

$c^ 2 = 81 + 144$

$c^ 2 = 225$

Taking the square root:

$c = \sqrt { 225}$

$c = 15 \space \text { cm}$

Thus, for this triangle, $$c$$ (the hypotenuse) is $$15 \space \text { cm}$$.

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