Pythagoras theorem is a formula that helps us determine the missing side of a triangle, with the measure of two sides, given.
The Pythagoras theorem formula is expressed as:
[tex](\small\text{Hypotenuse})^{2} = (\small\text{side}_{1} )^{2} + (\small\text{side}_{2} )^{2}[/tex]
Now, let us take an example to understand the concept better.
Example:
A triangle with longest side given as 15 centimeters. The base of the triangle has a length of 9 centimeters. What is the measure of the height?
Solution:
We are given the following:
- Longest side (hypotenuse of the triangle) = 15 cm
- Base of the triangle (Not the longest side) = 9 cm
When we plug the hypotenuse and the base, in the formula, we get;
Subtract 9² on both sides of the equation to isolate (side₂)².
- ⇒ 15² = 9² + (side₂)²
- ⇒ 15² - 9² = 9² + (side₂)² - 9²
We can use the rule [a² - b² = (a - b)(a + b)] to simplify the L.H.S
- ⇒ (15 - 9)(15 + 9) = (side₂)²
- ⇒ (6)(24) = (side₂)²
- ⇒ 144 = (side₂)²
Now, take square root on both sides of the equation to determine the measure of the missing side (height of triangle).
- ⇒ √144 = √(side₂)²
- ⇒ 12 = side₂
Therefore, the measure of the height is 12 centimeters.
Learn more about Pythagoras theorem: https://brainly.com/question/343682
