Question 892897: In a triangle ABC, ab=25 cm BC=125 cm. If ac is an integer in cm, then find the number of possible measures of ac.
Answer:
Ac may be hypotenuse or
Ac may be one side
So only two measures are possible.
But options given are: 22, 23, 48 & 49.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! numbers don't make sense.
the sum of any 2 sides of the triangle have to be greater than the third side.
this means that the third side has to be less than 150.
the difference of any 2 sides of the triangle have to be less than the third side.
this means that the third side has to be greater than 100.
none of your options are possible with those requirements.
an example of a legitimate triangle would be a 3,4,5 triangle.
the sum of 3 and 4 is > 5
the sum of 3 and 5 is > 4
the sum of 4 and 5 is > 3
the difference of 5 and 3 is less than 4
the difference of 5 and 4 is less than 3
the difference of 4 and 3 is less than 5
all the requirements are met.
that will not be the case with your triangle.
take the biggest possible side of 49.
59 + 25 is not bigger than 125.
end right there since any one of the requirements not being met will disqualify the side as being possible.
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