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

Question

?

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.