I know the formula is a^2+b^2=c^2 with a and b being legs and c being the hypotenuse. My question is why are the squares necessary? If everthing is squared, wouldn't that be the same as just a+b=c? I am so confused.
2007-09-10 04:05:09 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
No, this does not work. This is because (a + b)^2 is NOT the same as a^2 + b^2, so you can not just cancel the squares as you suggested. I'm sure you're familiar with the concept of FOILing, so let's FOIL (a + b)^2 to show that you would be missing a term if you simply said it was equal to a^2 + b^2:
(a + b)^2
==> write as two binomials
(a + b)(a + b)
==> FOIL: first, outside, inside, last
a^2 + ab + ab + b^2
==> combine like terms
a^2 + 2ab + b^2 ... This is NOT equal to a^2 + b^2
Therefore, you cannot simply cancel the squares on both sides. Hope that helps.
2007-09-10 04:09:54 · answer #1 · answered by C-Wryte 4 · 0⤊ 1⤋
No. Example 2+3=5 2^2 + 3^2 = 13
5 is not the square root of 13
2007-09-10 04:11:49 · answer #2 · answered by Anonymous · 0⤊ 0⤋
This formula is the result of Pythagoras' Theorem, look on Wiki for more info on that.
The squares are necessary because in general,
root(a²+b²)=/=a+b try a=b=1; root(1²+1²)=root(2) but a+b=1+1=2.
2007-09-10 04:18:32 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Definition: Isosolese triangle is a triangle with 2 factors of an identical length Hypotenuse is the side straight away opposite of a proper perspective. If it has the two features then whilst the pythagorean theorem (axa) +(bxb) = (cxc) works in this occasion a = b. subsequently you are able to replace b with a. So the formulation may well be (axa) + (axa) = (cxc) that's comparable to 2(axa)=(cxc) Or c... the hypotenuse is comparable to the sq. root of (2 cases "a" squared) the place a is the scale of yet another side.
2016-12-13 05:08:28 · answer #4 · answered by ? 4 · 0⤊ 0⤋
If you take a+b = c
then (a+b)^2 = c^2
i.e., a^2+b^2+2ab = c^2, which is not the case.
It is a^2+b^2 = c^2
There is a difference of 2ab.
So you have to tak the hypotenuse as
c = sqrt (a^2+b^2)
2007-09-10 04:14:49 · answer #5 · answered by Eechhutti 2 · 0⤊ 0⤋
No.. and you could answer your own question simply by plugging in some numbers and checking.
1+2 = 3
But does 1^2+2^2=3^2?
No. It = 5, and 3^2 = 9.
2007-09-10 04:13:42 · answer #6 · answered by nixity 6 · 0⤊ 0⤋
no, you will not get the correct answer , because you will have to first square a and b and then add their squares.IT ACTUALLY MAKES A LOT OF DIFFERENCE IN THE CALCULATION.
EXAMPLE: 3^2+4^2=25--------------1)
3+4=7----------------------2)
IN THIS EXAMPLE, [2)]^2 IS NOT EQUAL TO 1)
2007-09-10 04:19:18 · answer #7 · answered by whitepaint 2 · 0⤊ 0⤋
no its not the same, this is a formula invented by Pitagora, which is proved to be exact , dont get confused, just learn the formula and keep it in your mind, its one of the most needed formulas in geometry , is like the base of it!
2007-09-10 04:15:27 · answer #8 · answered by Anonymous · 0⤊ 0⤋
in order to get your hypotenuse you need to sqare a and b... it is the formaula and how you get your hypotenuse answer correct.
2007-09-10 04:11:30 · answer #9 · answered by somethingcorporate<3 1 · 0⤊ 0⤋
If you think it is the same, try it out and see if it works, then you will know.
.
2007-09-10 04:11:55 · answer #10 · answered by Robert L 7 · 0⤊ 0⤋