Perimeter, Area, and the Pythagorean Theorem

Perimeter, Area, and the Pythagorean Theorem

On the GED math test, you are provided with a formula sheet, but understanding when and how to apply each formula is essential.

Pythagorean Theorem

For any right-angled triangle with legs $a$ and $b$ and hypotenuse $c$:

$$a^2 + b^2 = c^2$$

Key Rule: The hypotenuse $c$ is always the longest side, directly opposite the 90-degree right angle.

Example Problem:

A ladder leans against a vertical wall. The base of the ladder is 6 feet from the wall, and the top reaches 8 feet high on the wall. How long is the ladder?

$$a = 6, \quad b = 8$$ $$6^2 + 8^2 = c^2$$ $$36 + 64 = 100$$ $$c = \sqrt{100} = 10 \text{ feet}$$