Question 759074: This is an old regents question that I need help with:
In the diagram of ABC, D is a point on AB , AC = 7, AD = 6, and BC = 18. The length of DB could be
1] 5 [3] 19
[2] 12 [4] 25
I tried to do the Pythagorean theorem but I just got this humongous number that was impossible to divide. I also tried to add it to 180,but I think that's only for angles and the numbers didn't calculate right.
Can you please help me?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Pythagoras can't help you here because this is not necessarily a right triangle. It could be, given precisely the correct measure for DB -- it would have to be  , but that is an irrational number hence not one of your choices.
This is a Triangle Inequality Problem. The Converse of the Triangle Inequality Theorem says that you cannot form a triangle if one of the sides is greater than or equal to the sum of the other two sides.
The sum of BC and AC is 18 + 7 = 25, hence AB must be strictly less than 25.
Also, the sum of AB and AC must be strictly less than 18, but since AC is 7, we can say that AB must be strictly less than 11.
So, in summary, we have
Subtracting 6, the measure of AD, from each part of the inequality and noting that DB = AB - AD, we get
And only one of your answers fits in that range.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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