Question 759074
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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 *[tex \LARGE 5\sqrt{11}\ -\ 6], 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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 11\ <\ AB\ <\ 25]


Subtracting 6, the measure of AD, from each part of the inequality and noting that DB = AB - AD, we get


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5\ <\ DB\ <\ 19]


And only one of your answers fits in that range. 


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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