EgmatQuantExpert wrote:
In the figure shown above, \(x\) is the length of side \(BD\) of triangle \(ABD\). If \(D\) is a point that lies on line \(AC\) and \(x\) is an integer, what is the value of \(x\)?
A. \(2\)
B. \(3\)
C. \(4\)
D. Both \(3\) and \(4\) are possible values for \(x\)
E. Cannot be determined
IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and BConsider ∆ABC
The two known sides have lengths 2 and 2
So, applying the above
rule, 2 - 2 < x < 2 + 2
In other words, 0 < x < 4
IMPORTANT: We're told that x is an
integer.
So the possible values of x are 1, 2 and 3
Now consider ∆BDC
The two known sides have lengths 4 and 2
So, applying the above
rule, 4 - 2 < x < 4 + 2
In other words, 2 < x < 6
Since x is an
integer, the possible values of x are 3, 4, and 5
So, x must be 1, 2 or 3 AND x must be 3, 4 or 5
Since x = 3 is the only value that satisfies both conditions, x must equal 3
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