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

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Re: In the figure above, what is the product of the lengths of A [#permalink]
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]
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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?
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Re: In the figure above, what is the product of the lengths of A [#permalink]
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]
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]
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]
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]
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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]
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Re: In the figure above, what is the product of the lengths of A [#permalink]
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