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Geometry

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by aplavakarthik » Tue Aug 16, 2011 3:38 am
In the figure, ABC and ADC are right triangles. Which of the following could be the lengths of AD and DC, respectively?

(I) 3 and 4
(II) 4 and 6
(III) 1 and 24
(IV) 1 and 26

(A) I and II only
(B) II and III only
(C) III and IV only
(D) IV and I only
(E) I, II and III only

Image

I dont think option IV satisfies
Answer: c
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by sl750 » Tue Aug 16, 2011 4:53 am
Answer is A

In III and IV, the side with length 1 will not satisfy the condition that the side should have a length that is in between the difference and sum of the other two sides
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by Tani » Tue Aug 16, 2011 7:59 am
GMAT often tests the Triangle Inequality Theorem. In this problem we know AC = 5 (ABC is a 3:4:5 triangle).

Looking at the other triangle, the Inequality theorem tells us:

|CD-AD|< AC <|CD+AD|

Only I and II meet this requirement.

Answer A

(By the way, triangle ACD doesn't have to be a right triangle. The Inequality Theorem applies to all triangles.)
Tani Wolff
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by gmatboost » Wed Aug 17, 2011 1:41 pm
Umm, if ADC is a right triangle as well, the only option that works is 3-4-5.

4-5-6 is not a right triangle.
Neither is 1-5-24 and 1-5-26

Maybe the question said (or meant to say) root(24) and root(26) ?
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