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In the figure above, what is the product of the lengths of AD and BC?
(1) The product of the lengths of AC and BE is 60.
(2) The length of BC is 8.
Attachment:
triangle.png [ 2.62 KiB | Viewed 8990 times ]
In the figure above, what is the product of the lengths of AD and BC?
Question: BC*AD=? Note that AD is perpendicular to BC and BE is perpendicular to AC. So: \(\frac{BC*AD}{2}=\frac{base*height}{2}=area\) and similarly \(\frac{AC*BE}{2}=\frac{base*height}{2}=area\) --> \(\frac{BC*AD}{2}=\frac{AC*BE}{2}\) --> \(BC*AD=AC*BE\).
(1) The product of the lengths of AC and BE is 60 --> AC*BE=60=BC*AD. Sufficient.
(2) The length of BC is 8. Not sufficient.
Answer: A.
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General Discussion
jlgdr
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,296
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,296
fluke
Yes one should keep in mind that a triangle of this type has three heights and three bases so one can calculate the area with any of those two perpendicular measures. Hence BC*AC / 2 = AC*BE /2
Hence A
1/2 * AD * BC = 1/2 * BE * AC = Area of the triangle
Statement 1 is sufficient
Statement 2 is not
Hence A
Statement 1 is sufficient
Statement 2 is not
Hence A
Posts: 652
Bunuel
With statement 2 saying the length of BC is 8, why can't we use the ratios of lengths in a right angle triangle and then calculate the product?
With statement 2 saying the length of BC is 8, why can't we use the ratios of lengths in a right angle triangle and then calculate the product?
MsInvBanker
Different right triangles have different ratio of the lengths of their sides.
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Bunuel
Agreed. But this is definitely the 30, 60, 90 triangle. So we can apply the relevant ratio and figure out the lengths.
MsInvBanker
No, you cannot assume that it's 30-60-90 triangle.
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fluke
Hi VeritasKarishma, can you help me please?
Looking at the figure, can we assume that AD and BE are the median's of the triangle?
Also, is there another way to solve this problem?
Thanks :D
exc4libur
No, there is no reason to believe that AD and BE are medians. We only know that they are altitudes.
The area of the triangle is a very useful concept.
Area of triangle = (1/2)* AD * BC = (1/2)* BE * AC
Stmnt 1: If AC * BE = 60, then AD * BC = 60 too.
Sufficient.
Stmnt 2: The length of BC is 8.
AD is unknown. Not sufficient.
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