# Hypotenuse ???

• May 5th 2007, 01:01 PM
whytechocolate01
Hypotenuse ???
The legs of a right triangle are 3 and 4. Find the length of the hypnotuse.... :confused: Please explain!

WhyteChocolate
• May 5th 2007, 01:05 PM
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!
• May 5th 2007, 01:09 PM
Jhevon
Quote:

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)
• May 5th 2007, 01:15 PM
Jhevon
Quote:

Originally Posted by whytechocolate01
The legs of a right triangle are 3 and 4. Find the length of the hypnotuse.... :confused: Please explain!

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
• May 5th 2007, 01:32 PM
Geometor
Quote:

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)

:D 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.
• May 5th 2007, 01:34 PM
Jhevon
Quote:

Originally Posted by Geometor
:D 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)