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In the figure above, what is the product of the lengths of A

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In the figure above, what is the product of the lengths of A [#permalink] New post   30 Jan 2011, 06:18
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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.


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In the figure above, what is the product of the lengths of A [#permalink] New post   30 Jan 2011, 06:31
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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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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   08 Oct 2018, 12:00
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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?
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   14 Nov 2019, 06:06
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exc4libur wrote:
fluke wrote:


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.


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


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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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   10 Jan 2014, 14:28
fluke wrote:


20. 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.


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
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   19 Dec 2015, 23:39
1/2 * AD * BC = 1/2 * BE * AC = Area of the triangle

Statement 1 is sufficient
Statement 2 is not

Hence A
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   08 Oct 2018, 21:08
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MsInvBanker wrote:
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?


Different right triangles have different ratio of the lengths of their sides.
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   08 Oct 2018, 23:17
Bunuel wrote:
MsInvBanker wrote:
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?


Different right triangles have different ratio of the lengths of their sides.


Agreed. But this is definitely the 30, 60, 90 triangle. So we can apply the relevant ratio and figure out the lengths.
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   08 Oct 2018, 23:35
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MsInvBanker wrote:
Bunuel wrote:
MsInvBanker wrote:
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?


Different right triangles have different ratio of the lengths of their sides.


Agreed. But this is definitely the 30, 60, 90 triangle. So we can apply the relevant ratio and figure out the lengths.


No, you cannot assume that it's 30-60-90 triangle.
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   14 Nov 2019, 05:48
fluke wrote:


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.


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
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Re: In the figure above, what is the product of the lengths of A [#permalink] New post   11 Apr 2022, 07:53
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Re: In the figure above, what is the product of the lengths of A [#permalink]
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