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### Course: 8th grade (Illustrative Mathematics)>Unit 8

Lesson 8: Lesson 8: Finding unknown side lengths

# Pythagorean theorem intro problems

Practice using the Pythagorean theorem to solve for missing side lengths on right triangles.  Each question is slightly more challenging than the previous.

## Pythagorean theorem

The equation for the Pythagorean theorem is
a, squared, plus, b, squared, equals, c, squared
where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

## Practice problems

Problem 1
• Current
Find the value of x in the triangle shown below.

Want more Pythagorean theorem practice? Check out this exercise.

## Want to join the conversation?

• Is there any way on how to do Pythagorean theorem easier im having trouble understanding
• You can remember easy "Pythagorean Triples" like the famous 3-4-5 combo, with 5 being the hypotenuse. There are also some other not-as-famous triples like the 5-12-13 triple, the 7-24-25 triple, and the 9-40-41. Note that the hypotenuse of these "triples" is always the largest number.
• there is so much history in the comments
• this was disrespectful
(1 vote)
• i wonder how we figured out the pythagoream theorem
• It was proven by Pythagoras. There are several popular proofs (even one done by a former US president [Garfield]). Look up proof of Pythagoras Theorem on YouTube.
• Just a quick question, so in a test it could say find the distance of the other 2 sides of the triangle. Can you find out the other 2 sides using the pythagorean theorem or is there another way to find that out?
• There is no way to do it if you are only given 1 side :(
• So, for the Pythagorean Theorem you do a squared plus b squared equals c squared. Why is a+c=b a thing? I don't get it.
• a+c cannot equal b. This is because c is the hypotenuse. Instead, you could do c²-a²=b².
• how can i find the b (the one one the side thats straight)
• you would instead do c^2-a^2=b^2. if you are missing "a" you can also swap those and do c^2 - b^2 = a^2