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# Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a

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Math Expert
Joined: 02 Sep 2009
Posts: 49300
Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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02 Sep 2018, 23:12
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Difficulty:

25% (medium)

Question Stats:

86% (01:17) correct 14% (00:54) wrong based on 21 sessions

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Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° and angle CBD is 45°, how much longer is AB than DC?

(1) The length of BC is 12.
(2) The length of CA is 6.

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Math Expert
Joined: 02 Aug 2009
Posts: 6797
Re: Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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02 Sep 2018, 23:55
1
Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° and angle CBD is 45°, how much longer is AB than DC?

triangle ACB is 30-60-90 so sides are $$1:\sqrt{3}:2=AC:AB:BC$$ and triangle DCB is 45-45-90 so sides are $$1:1:\sqrt{2}=CD:DB:BC$$
Thus all 6 lines are interconnected. Knowing one side can give us all length and thus AB-DC also

(1) The length of BC is 12.
BC=12
we can know all sides
suff

(2) The length of CA is 6.
AC=6
we can know all sides
suff

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 02 Jun 2018
Posts: 13
Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a  [#permalink]

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03 Sep 2018, 00:40

Triangle CBD us isoceles.

And hence with one side bc we can find bd or CD - statement 1

With AC and BC we can find AB.

Hence we can find the difference.

So both statement together can find the result

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Right triangles CAB and CDB share hypotenuse CB. If angle ACB is 60° a &nbs [#permalink] 03 Sep 2018, 00:40
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