Question

Which of the following correctly uses the Pythagorean Theorem to find the missing side
?

A
�2+(10)2=82x^{2}+\left(10\right)^{2}=8^{2}x
2
+(10)
2
=8
2

B
�+8=10x+8=10x+8=10
C
�2+82=(10)2x^{2}+8^{2}=\left(10\right)^{2}x
2
+8
2
=(10)
2

D
82+(10)2=�28^{2}+\left(10\right)^{2}=x^{2}8
2
+(10)
2
=x
2

Answer 1

To find the missing side using the Pythagorean Theorem, we need to remember the theorem itself, which states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), the relationship is given by:

\[
a^2 + b^2 = c^2
\]

Let's analyze each option:

**Option A**: \( x^2 + (10)^2 = 8^2 \)

Here, you are trying to solve for \( x \), assuming 10 is one leg and 8 is the hypotenuse. However, 8 should not be the hypotenuse since it's less than 10. This is incorrect.

**Option B**: \( x + 8 = 10 \)

This is not using the Pythagorean theorem since it's not in the form of \( a^2 + b^2 = c^2 \). This is simply a linear equation. Thus, this is incorrect.

**Option C**: \( x^2 + 8^2 = (10)^2 \)

This correctly sets up the equation based on the Pythagorean theorem. Here, if we consider 10 as the hypotenuse and 8 as one of the legs, this makes sense. This option is valid.

**Option D**: \( 8^2 + (10)^2 = x^2 \)

This does not follow the Pythagorean theorem. In this case, one side cannot be greater than the hypotenuse. This option is also incorrect.

Given the options:

- **C** is the correct usage of the Pythagorean Theorem to find the missing side, where \( x^2 + 8^2 = 10^2 \).