Question

Describe and correct the error in using the Pythagorean Theorem.

Answer 1

The Pythagorean theorem states that the square of the hypothenuse is equal to the sum of squares of the sides of the right triangle.

You can express the theorem as:

`a^2+b^2=c^2`

The triangle in the picture has the following side measures:

Hypothenuse c = 26

Side a = 10

Side b = x

To calculate the missing value using the Pythagorean theorem you have to write it for "b" first:

`a^2+b^2=c^2`

-First, subtract a² to both sides of the equation

`\begin{gathered} a^2-a^2+b^2=c^2-a^2 \\ b^2=c^2-a^2 \end{gathered}`

-Second, calculate the square root to both sides of the expression so that it is expressed for b

`\begin{gathered} \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}`

-Third replace the expression with the known side lengths:

`\begin{gathered} x=\sqrt[]{26^2-10^2} \\ x=\sqrt[]{676-100} \\ x=\sqrt[]{576} \\ x=24 \end{gathered}`

The length of the missing side is 24 units.

The error committed in the steps shown in the picture is that the Pythagorean theorem was applied as if the missing side was the hypothenuse of the right triangle instead of being one of its legs.