When asked to factor the x^2-121 a student gives the answer (x-11)(x-11) what is wron with this answer?
2 answers:
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Okay so lets look at the equation given
this is the Pythagorean theorem, this equation holds true to all right angle triangles.
for the "a" and "b" terms must be the two shortest lengths and "c" must be the longest length.
why? because "c" represents the hypotenuse in this theorem and the hypotenuse is by definition the longest side of a right triangle.
(side note: always draw a picture, it helps a lot if you doodle a bit to get an idea of what you are working with)
we are given three lengths : 3 , 4, and 5 (im ignoring the measurements for now)
we can look at it two ways with a picture and through algebra
try to draw a right triangle with the given info. you'll see there are only two cases were this is possible the picture above is one case where this is not possible
now we can look at this algebraically
(but "a" and "b" can swap lengths)
now with the Pythagorean theorem we can see how this plays out
and heres with "a" and "b" lengths swapped
now here's a case when we let 5 , our longest length , become a leg and let one our shorter lengths take the place of "c"
obviously 34 does not equal 16
hope this helped you out
this is the Pythagorean theorem, this equation holds true to all right angle triangles.
for the "a" and "b" terms must be the two shortest lengths and "c" must be the longest length.
why? because "c" represents the hypotenuse in this theorem and the hypotenuse is by definition the longest side of a right triangle.
(side note: always draw a picture, it helps a lot if you doodle a bit to get an idea of what you are working with)
we are given three lengths : 3 , 4, and 5 (im ignoring the measurements for now)
we can look at it two ways with a picture and through algebra
try to draw a right triangle with the given info. you'll see there are only two cases were this is possible the picture above is one case where this is not possible
now we can look at this algebraically
(but "a" and "b" can swap lengths)
now with the Pythagorean theorem we can see how this plays out
and heres with "a" and "b" lengths swapped
now here's a case when we let 5 , our longest length , become a leg and let one our shorter lengths take the place of "c"
obviously 34 does not equal 16
hope this helped you out