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In the right triangle above, what is the length of AC?

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In the right triangle above, what is the length of AC?  [#permalink]

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New post 21 Sep 2018, 00:17
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

73% (02:09) correct 27% (02:37) wrong based on 91 sessions

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Re: In the right triangle above, what is the length of AC?  [#permalink]

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New post 21 Sep 2018, 00:23
Bunuel wrote:
Image
In the right triangle above, what is the length of AC?

(A) 9
(B) 10
(C) 12
(D) 13
(E) 15


Attachment:
The attachment Capture (1).JPG is no longer available


Most frequent right triangles used in GMAT are as shown in attachment

Now we have to think of right triangle with sides (x-1), (x+2) and (x+5) i.e. sides with length separated by 3 units

As we see there is a right triangle 9-12-15 which fits

hence, x-1 = 9

i.e. x = 10

i.e. AC = x+2 = 12

Answer: Option C
Attachments

Geometry 5 Special right triangle1.jpg
Geometry 5 Special right triangle1.jpg [ 123.92 KiB | Viewed 1209 times ]


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Re: In the right triangle above, what is the length of AC?  [#permalink]

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New post 21 Sep 2018, 05:13
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Bunuel wrote:
Image
In the right triangle above, what is the length of AC?

(A) 9
(B) 10
(C) 12
(D) 13
(E) 15


Attachment:
Capture (1).JPG


Since we have a right triangle, we can apply the Pythagorean Theorem
When we do so we get: (x - 1)² + (x + 2)² = (x + 5)²
Expand each square to get: (x² - 2x + 1) + (x² + 4x + 4) = x² + 10x + 25
Simplify left side to get: 2x² + 2x + 5 = x² + 10x + 25
Subtract x² from both sides to get: x² + 2x + 5 = 10x + 25
Subtract 10x from both sides to get: x² - 8x + 5 = 25
Subtract 25 from both sides to get: x² - 8x - 20 = 0
Factor: (x - 10)(x + 2) = 0
So, EITHER x = 10 OR x = -2

We can rule out the solution x = -2, since that would make some of the lengths NEGATIVE
So, it MUST be the case that x = 10

AC has length x + 2
So, AC = 10 + 2 = 12

Answer: C

Cheers,
Brent
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Re: In the right triangle above, what is the length of AC?  [#permalink]

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New post 21 Sep 2018, 06:31
Bunuel wrote:
Image
In the right triangle above, what is the length of AC?

(A) 9
(B) 10
(C) 12
(D) 13
(E) 15


Attachment:
Capture (1).JPG


? = AC = x+2 = greatest leg (I mean, the bigger leg between the two! I don´t know if my English was understood...)

First of all, let´s LOOK at the dimensions... we have two legs that differ by 3 units, hypotenuse 6 units greater than the shorter leg...

3,4,5 does not work (legs one unit apart)... what about "three times it" (so that legs will be three units apart)? 3*3, 4*3, 5*3 ... DONE!

(Reason: 9 and 12 differ by 3 units, 15 is 6 units greater than 9... we are sure we have a right triangle, because "3k, 4k, 5k" always is...)

? = 12 (the greatest leg)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: In the right triangle above, what is the length of AC?  [#permalink]

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Re: In the right triangle above, what is the length of AC?   [#permalink] 23 Sep 2019, 06:30
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