Page 245 - ABCTE Study Guide_Neat

All right, let’s see how to use the theorem. Suppose the two legs of a right triangle measure 3 in. and 4 in.
What is the length of the hypotenuse? In the theorem, a and b represent the lengths of the legs, so let a =
3 and b = 4. Now find c:

The hypotenuse is 5 inches in length.

A 3-4-5 triangle is the most popular Pythagorean triple. A Pythagorean triple is a set of three positive
integers that satisfy the Pythagorean Theorem. Multiples of Pythagorean triples are also Pythagorean
triples. In other words, since 3-4-5 is a Pythagorean triple, so is 6-8-10 and 9-12-15. Another Pythagorean
triple is 5-12-13.

Most, if not all, test questions related to the Pythagorean Theorem involve Pythagorean triples, because
they’re easier to compute and they don’t involve irrational numbers (like or ).

Question:

One leg of a right triangle is 8 cm long and its hypotenuse measures 17 cm. What is the length of the
remaining leg?

A 9 cm

B 11 cm

C 15 cm

D 19 cm

Answer

Choice C is the correct answer. The Pythagorean Theorem states that , where a and b are
the lengths of the legs of a right triangle, and c is the length of the hypotenuse. In this problem, one leg
measures 8 cm and the hypotenuse measures 17 cm. So, let a = 8 and c = 17, and find b.

The other leg has length 15 cm. Did you figure out that 8-15-17 is also a Pythagorean triple?