Question

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

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

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

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

D
�+8=10x+8=10x+8=10

Answer 1

To find the missing side using the Pythagorean Theorem, we need to correctly apply the formula \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides of a right triangle.

Let's analyze each option:

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

This correctly sets up the relationship as \(8^2 + 10^2 = x^2\), since 10 is likely the hypotenuse if 8 and the missing side \(x\) are the other two sides. This option correctly uses the Pythagorean theorem.

**B.** \(x^2 + (10)^2 = 8^2\)

This is incorrect because it implies that the hypotenuse is the shorter side (8) whereas \(10\) should be the hypotenuse in this case, given that it’s the longest side.

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

This correctly uses the theorem in the form \(x^2 + 8^2 = 10^2\), with \(10\) being the hypotenuse and \(8\) and \(x\) as the other two sides. This is consistent with the Pythagorean theorem as well.

**D.** \(x + 8 = 10\)

This is not applying the Pythagorean theorem at all; it simply sets an algebraic equation, which doesn’t represent the sides of a right triangle.

Based on the analysis, both options **A** and **C** correctly use the Pythagorean Theorem to find the missing side.