Question

Three side lengths of a right triangle are given. Use the drop-down menus to explain why matters where you substitute the lengths in the Pythagorean Theorem.
In the Pythagorean Theorem, the two shortest sides
must always be substituted for the side lengths, not the hypotenuse.

(Am I correct, if yes, can you explain why)

Answer 1

Answer:

The Pythagorean Theorem is used for right triangles only, because it's a mathematical relation between the legs of the triangle and the hypothenuse, where each leg must be less than the length of the hypothenuse.

It's important to correctly identify each element of the triangle, that is, which sides are legs, and which side is the hypothenuse, because the Pythagorean Theorem has a specific order, that means, if we make a mistake identifying each element, then the result will be wrong.

For example, the expression $c^{2}=a^{2} +b^{2}$ is the theorem, where $c$ is the hypothenuse. This theorem states that the square of the hypothenuse (longest side) is equal to the sum of the square of the legs. So, if we call $c$ a leg instead of the hypothenuse, the theorem won't work.