Mathematics Knowledge

Yesterday I presented a question about the hypotenuse of a triangle.

What is the hypotenuse of a right triangle with 2 sides measuring 30 and 40?

  1. 50
  2. 60
  3. 70
  4. 80

Do you know what the answer is?

In working as an ASVAB tutor, I place a strong emphasis on the review of triangles.  The subtopic of triangles is one of the 15 subtopics I cover when I review Mathematics Knowledge.  This question is about a right triangle.  It presents the measure of two sides of a right triangle.  The measure of the third side needs to be figured out.  The missing side is the longest side of the triangle, also known as the hypotenuse.  To figure out the measure of the third side, you can use the Pythagorean theorem.

The Pythagorean theorem is c2 = a2 + b2

a and b are the shorter sides and c is the longer side.

The shorter sides are 30 and 40

c2 = 302 + 402

c2 = 900 + 1600

c2 = 2500

c = Ö2500 = 50

There is an easier way to solve this problem.

I remind my students to memorize the measures of common right triangles

3:4:5          5:12:13

6:8:10       10:24:26

If the 3:4:5 triangle was made 10 times larger, it would be a 30:40:50 triangle.

The largest side would be 50.  I could have solved it without using the Pythagorean theorem to save time.