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# If a right triangle has 2x and 2x+1, what is the length of BC, in term

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Math Revolution GMAT Instructor
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If a right triangle has 2x and 2x+1, what is the length of BC, in term  [#permalink]

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21 Feb 2016, 22:05
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80% (00:58) correct 20% (01:13) wrong based on 54 sessions

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If a right triangle has 2x and 2x+1, what is the length of BC, in terms of x?

A. 4x-1
B. 4x+1
C. √(4x-1)
D. √(4x+1)
E. 4x

* A solution will be posted in two days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 20 Feb 2015 Posts: 726 Concentration: Strategy, General Management Re: If a right triangle has 2x and 2x+1, what is the length of BC, in term [#permalink] ### Show Tags 22 Feb 2016, 06:50 using pythagoras theorem we have (BC)2 =(AC)2-(AB)2 BC = root(4x+1) Manager Joined: 09 Jul 2013 Posts: 107 If a right triangle has 2x and 2x+1, what is the length of BC, in term [#permalink] ### Show Tags 22 Feb 2016, 10:29 CounterSniper wrote: using pythagoras theorem we have (BC)2 =(AC)2-(AB)2 BC = root(4x+1) CounterSniper nailed it. Here it is with the proper formatting: $$(AC)^2 = (AB)^2 + (BC)^2$$ $$(2x+1)^2 = (2x)^2 + (BC)^2$$ $$4x^2 + 4x+ 1 = 4x^2 + (BC)^2$$ $$(BC)^2 = 4x+1$$ $$BC = \sqrt{4x+1}$$ Answer: D _________________ Dave de Koos GMAT aficionado CEO Joined: 20 Mar 2014 Posts: 2550 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) If a right triangle has 2x and 2x+1, what is the length of BC, in term [#permalink] ### Show Tags 22 Feb 2016, 10:51 davedekoos wrote: CounterSniper wrote: using pythagoras theorem we have (BC)2 =(AC)2-(AB)2 BC = root(4x+1) CounterSniper nailed it. Here it is with the proper formatting: $$(AC)^2 = (AB)^2 + (BC)^2$$ $$(2x+1)^2 = (2x)^2 + (BC)^2$$ $$4x^2 + 4x+ 1 = 4x^2 + (BC)^2$$ $$(BC)^2 = 4x+1$$ $$BC = \sqrt{4x+1}$$ Answer: D An alternate way would be to substitute x=1 to get the 2 given sides as 2x=2 units and 2x+1=9, giving you the other side = $$\sqrt{9-4}$$ = $$\sqrt{5}$$ Analyse options, A. 4x-1 = 3 . Eliminate B. 4x+1 = 5. Eliminate C. √(4x-1) = $$\sqrt{3}$$. Eliminate D. √(4x+1) =$$\sqrt{5}$$. Keep. E. 4x= 4. Eliminate. Thus D is the correct answer. Hope this helps. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8475 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a right triangle has 2x and 2x+1, what is the length of BC, in term [#permalink] ### Show Tags 23 Feb 2016, 18:35 If a right triangle has 2x and 2x+1, what is the length of BC, in terms of x? A. 4x-1 B. 4x+1 C. √(4x-1) D. √(4x+1) E. 4x -> (2x)2+(BC)2=(2x+1)2, (BC)2=4x2+4x+1-4x2=4x+1, BC=√(4x+1). Therefore, the answer is D. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If a right triangle has 2x and 2x+1, what is the length of BC, in term   [#permalink] 23 Feb 2016, 18:35
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# If a right triangle has 2x and 2x+1, what is the length of BC, in term

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