EZ Math

Geometry · Angles and triangles

How to Use the Pythagorean Theorem

Problem

legs 6 and 8\text{legs } 6 \text{ and } 8

Answer

c=10c = 10

The Pythagorean theorem works only in a right triangle. The two shorter sides are the legs, and the longest side is the hypotenuse.

Step-by-step solution

  1. Write the Pythagorean theorem.

    a2+b2=c2a^2 + b^2 = c^2

    Why: The theorem links the two legs and the hypotenuse of a right triangle.

  2. Substitute the legs and add the squares.

    62+82=c2⇒36+64=1006^2 + 8^2 = c^2 \Rightarrow 36 + 64 = 100

    Why: The hypotenuse is unknown, so it stays as c.

  3. Take the square root.

    c=100=10c = \sqrt{100} = 10

    Why: A length uses the positive square root.

Common mistakes

  • Adding the legs before squaring: 6 + 8 = 14.
  • Squaring the sum of the legs.
  • Forgetting the square root at the end.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. legs 3 and 4\text{legs } 3 \text{ and } 4

    Show answer

    c=5c = 5

  2. legs 5 and 12\text{legs } 5 \text{ and } 12

    Show answer

    c=13c = 13

  3. legs 9 and 12\text{legs } 9 \text{ and } 12

    Show answer

    c=15c = 15

  4. legs 7 and 24\text{legs } 7 \text{ and } 24

    Show answer

    c=25c = 25

  5. legs 8 and 15\text{legs } 8 \text{ and } 15

    Show answer

    c=17c = 17