Question

The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.

4
11
13
12

Answer 1

12

Explanation:

Right triangles can be solved using the Pythagorean theorem.

Pythagorean Theorem

The Pythagorean theorem says
`a^(2) +b^(2)= c^(2)`, where a and b are shorter sides and c is the hypotenuse (the longest side of a right triangle). We can plug the values into the theorem to find the missing side.

• 
  `5^(2) +b^(2) =13^(2)`

Then solve for b

• b = ±12

However, since length cannot be negative, the missing side must be 12.

Pythagorean Triples

Pythagorean triples are 3 positive integers that form a right triangle and satisfy the Pythagorean theorem. Some common triples include (3,4,5) and (5,12,13). Memorizing these common triples can help you answer questions about right triangles.