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## Algebra basics

### Course: Algebra basics>Unit 8

Lesson 3: Pythagorean theorem

# Pythagorean theorem example

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse). We can apply the theorem to find the missing side length of a right triangle, even when the missing length is one of the shorter sides. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• I was wondering can i just solve the problem like this??
a 2+9 2=14 2
so 14 -9 = 5
so can't it be 5 squared???( 5 2 )
• wow reading this... it says 11 years ago
• Why didn't Sal just go all the way and square root 115? Are you not supposed to have a decimal?
• That’s a good question. Most of what is taught here is what we call theoretical math. The convention for this, is to express an answer in the simplest format. To express an answer as root 115 is a lot cleaner and actually more accurate than the decimal form (10.72380529…). Now, if you need to actually apply this number to a physical object; say you need to measure the length of something, the decimal format would better suit this.
• i really dont get y we need this like i am good without this in my life
• This is a fundamental part of architecture, buildings, etcetera. If you don't like this, then you'll never be able to buy a proper house and be easily scammed.
• How do you calculate a square root without a calculator ? Is it possible ?
• Daphne78, it is possible. For example, (-5)*(-5)=25, also 5*5=25. So √25 can either be (-5) or 5.
• So when he says Square root of 115 he means 23 as the answer or just 115 why did he say 115 is the answer? Is there a rule behind it, if the numbers square rooted from the original number are prime then the original number is the answer
?
• Square root of 115 equals 10.723..., not 23. Because square root of 115 is not a whole number, we just keep it written as √115.
• So is the Pythagorean theorem for other triangles too, or just for the right triangles?
• The Pythagorean theorem applies to right triangles only.

It is true that some problems involving non-right triangles can be solved using the Pythagorean theorem indirectly, but only by creating right triangles. For example, given the sides of an isosceles triangle, one can find the altitude to the unequal side by drawing this altitude, and then using the Pythagorean theorem on one of the two congruent right triangles formed by this altitude.

Have a blessed, wonderful day!
• But can you solve the question if i just give you the hypotenuse and another side to solve the third side?
• Yes. You can use the Pythagorean theorem to solve for a missing side.
• if we had a left 90o degree triangle, would the Pythagorean theorem work????
• The Pythagorean theorem ONLY works on 90 degree triangle aka right triangle.
• Why didn’t he just go All the way to square root your supposed to have a decimal.
• You know about irrational numbers where the decimal goes on forever?

Which would you rather see? Sqrt(15) or 10.7238052948? Imaging performing operations on such a long decimal!

Decimals are not always preferred in maths (especially in algebra) for this reason. It's preferred that you leave it as a root or fraction to make the working easier.