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

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New post 21 Feb 2016, 22:05
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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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Re: If a right triangle has 2x and 2x+1, what is the length of BC, in term  [#permalink]

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New post 22 Feb 2016, 06:50
using pythagoras theorem we have
(BC)2 =(AC)2-(AB)2
BC = root(4x+1)
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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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New post 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
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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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New post 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.
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Re: If a right triangle has 2x and 2x+1, what is the length of BC, in term  [#permalink]

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New post 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.
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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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