Thread: Hypotenuse ???

The legs of a right triangle are 3 and 4. Find the length of the hypnotuse.... Please explain!

Thanks in advance.
WhyteChocolate

The hypotenuse is the longest side of a triangle and is opposite the right-angle in a right-angled triangle. From what you tell me, Phythagoras theorem shall be used here. Where:

c^2 = a^2 + b^2 (note, a b and c can be any value) in this case the c represents the hypotenuse (its the longest side)

so, you have 3 and 4 as the other lengths. THat means
c^2 = 3^2 + 4^2
= 9 + 16
= 25
c = sq. root 25
= 5

Happy to help!

Originally Posted by Geometor

The hypotenuse is the longest side of a triangle and is opposite the right-angle in a right-angled triangle. From what you tell me, Phythagoras theorem shall be used here. Where:

c^2 = a^2 + b^2 (note, a b and c can be any value) in this case the c represents the hypotenuse (its the longest side)

so, you have 3 and 4 as the other lengths. THat means
c^2 = 3^2 + 4^2
= 9 + 16
= 25
c = sq. root 25
= 5

Happy to help!

Geometor is absolutely right, but i'd just like to point out that this is the famous 3-4-5 triangle, so with experience you would know that the answer is 5 without doing any calculations. it works for anything in propotion as well.

so if the legs were: 12 and 16, the answer for the hypotenuse would be 20, without even doing calculations (you can check this if you don't believe me)

Originally Posted by whytechocolate01

The legs of a right triangle are 3 and 4. Find the length of the hypnotuse.... Please explain!

Thanks in advance.
WhyteChocolate

for the record, whenever you see a right-triangle, the first thing you should think of is Pythagoras' theorem, it's almost always the formula to use when dealing with problems of that nature

Originally Posted by Jhevon

Geometor is absolutely right, but i'd just like to point out that this is the famous 3-4-5 triangle, so with experience you would know that the answer is 5 without doing any calculations. it works for anything in propotion as well.

so if the legs were: 12 and 16, the answer for the hypotenuse would be 20, without even doing calculations (you can check this if you don't believe me)

thank you for adding on but to expand on your point. If 3-4-5 triangle exists in phythagoras theorem so there also is a 6-8-10 (2(3-4-5), 9-12-15(33-4-5) triangle. This may be useful when a question asks you to list the lengths of a triangle solved by pythagoras.

Originally Posted by Geometor

thank you for adding on but to expand on your point. If 3-4-5 triangle exists in phythagoras theorem so there also is a 6-8-10 (2(3-4-5), 9-12-15(33-4-5) triangle. This may be useful when a question asks you to list the lengths of a triangle solved by pythagoras.

you're right. that's the point i was making with my 12-16-20 triangle example, that is 4*(3-4-5)