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03 Jan 2016, 13:19
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:52) correct
31%
(02:00)
wrong
based on 282
sessions
History
Date
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Not Attempted Yet
In the diagram above, if the area of triangle LNO is 32, then what is the area of triangle LMN?
A. 24
B. \(24 \sqrt{2}\)
C. \(24 \sqrt{3}\)
D. 32
E. 48
Attachment:
2016-01-04_0017.png [ 10.43 KiB | Viewed 7186 times ]
04 Jan 2016, 14:55
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Bunuel
Even though the figure looks like a square, that can NEVER be assumed. It explicitly states that the figure is not drawn to scale (something we should assume all the time unless it is stated otherwise), and we must ONLY work with the information given.
Examining triangle LNO, we are given that the
\(area= \frac{base * height}{2} = 32\)
Since we have a right angle at O, we can consider the base to be LO and the height to be ON. We are given the height = 8, so the base, LO, is \(\frac{area*2}{base} = \frac{32*2}{8}=8\)
So, triangle LNO is an isosceles right triangle, and therefore the hypotenuse, LN, is \(8\sqrt{2}\)
Now looking at triangle LMN, we have the height given as 6, and the base LN calculated as \(8\sqrt{2}\), so
\(area=\frac{6*8\sqrt{2}}{2} = 24\sqrt{2}\)
Answer: B
Updated on: 23 May 2020, 06:18
Originally posted by BrentGMATPrepNow on 12 Aug 2016, 14:23.
Last edited by BrentGMATPrepNow on 23 May 2020, 06:18, edited 1 time in total.
Last edited by BrentGMATPrepNow on 23 May 2020, 06:18, edited 1 time in total.
Kudos
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Bunuel
First examine the blue triangle.
We're told the area = 32
Area = (base)(height)/2
So, 32 = (x)(8)/2
Solve to get: x = 8
Since the blue triangle is a right triangle, we can apply the Pythagorean Theorem to find the length of the hypotenuse.
We get: 8² + 8² = hypotenuse²
Simplify: 128 = hypotenuse²
So, hypotenuse = √128 = 8√2
We get:
At this point, we can focus on the red triangle
We can see that we now have the length of the base AND the height.
So, area of red triangle = (base)(height)/2
= (8√2)(6)/2
= 24√2
Answer:
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