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21 Sep 2018, 01:17
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C
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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 [ 22.98 KiB | Viewed 7285 times ]
21 Sep 2018, 01:23
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Bunuel
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 [ 123.92 KiB | Viewed 7264 times ]
21 Sep 2018, 06:13
Kudos
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Bunuel
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
