Geometry Tree shadow

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Layo: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Sep 14, 2010 6:58 am

by Layo » Thu Oct 20, 2011 9:51 am

As the figure shown above, the taller tree is 30 feet high and has a 40 feet shadow. What is the height of the shorter tree?
(1) The shorter tree has a 22 feet shadow.
(2) The distance between two trees is 18 feet.

OA D

Could you explain please?

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 20, 2011 9:51 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Thu Oct 20, 2011 9:59 am

Well looking at the options you should recognize that both of them actually give you the same data.

Now both are similar triangles.

you get x/30=40/22
x=16.5. Both options actually give you this data. D

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Thu Oct 20, 2011 10:24 am

ABC is a right triangle and
BC || DE

Statement 1 : The shorter tree has a 22 feet shadow.

EA/AC = DE/BC
22/40 = x/30
therefore 1st statement alone is sufficient

Statement 2 : The distance between two trees is 18 feet.
CE = 18
EA = AC - CE = 22
rest same as statement 1

Both the Satements alone are sufficient..

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Layo: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Sep 14, 2010 6:58 am

by Layo » Thu Oct 20, 2011 11:33 am

rijul007 wrote:

ABC is a right triangle and
BC || DE

Statement 1 : The shorter tree has a 22 feet shadow.

EA/AC = DE/BC
22/40 = x/30
therefore 1st statement alone is sufficient

Statement 2 : The distance between two trees is 18 feet.
CE = 18
EA = AC - CE = 22
rest same as statement 1

Both the Satements alone are sufficient..

Yeah, but how do you know that its a proportion? DE is not equidistant from BC

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Oct 20, 2011 12:12 pm

As the figure shown above, the taller tree is 30 feet high and has a 40 feet shadow. What is the height of the shorter tree?

Another approach

Assuming that Tree1 and Tree2 are Perpendicular to the ground, Triangles AED and ACB are Similar triangles.(AAA theorem) âˆ DAE = âˆ BAC ; âˆ DEA = âˆ BCA = 90. Since two angles of the triangle AED are equal to two angles of the triangle ACB, âˆ CBA = âˆ EDA.

So BC/DE = AC/AE BC = 30, DE = x, AE = ?, AC = 40

(1) The shorter tree has a 22 feet shadow.

=> AE = 22, BC/DE = AC/AE BC = 30, DE = x, AE = 22, AC = 40 and DE = 30*22/40

Sufficient

(2) The distance between two trees is 18 feet.

CE = 18 feet, AC = 40; AE = AC-CE = 40-18 = 22

=> AE = 22, BC/DE = AC/AE BC = 30, DE = x, AE = 22, AC = 40 and DE = 30*22/40

Sufficient

Answer : Option D

Note: If you are unaware of similar triangles click here https://www.mathopenref.com/similartriangles.html

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Thu Oct 20, 2011 11:52 pm

Layo wrote:
rijul007 wrote:

ABC is a right triangle and
BC || DE

Statement 1 : The shorter tree has a 22 feet shadow.

EA/AC = DE/BC
22/40 = x/30
therefore 1st statement alone is sufficient

Statement 2 : The distance between two trees is 18 feet.
CE = 18
EA = AC - CE = 22
rest same as statement 1

Both the Satements alone are sufficient..
Yeah, but how do you know that its a proportion? DE is not equidistant from BC

Thats because DE is parellel to BC
and it's a known fact that a line parellel to one of the sides cuts the other two in the same ratio.

here,
triangle ABC is similar to triangle ADE
so we can say that
AB/AD = AC/AE = BC/DE

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bpdulog: Master | Next Rank: 500 Posts; Posts: 105; Joined: Sun Jan 25, 2009 6:55 pmFollowed by: 1 member; Thanked: 2 times

by bpdulog » Fri Oct 21, 2011 7:52 am

D

They give you either 22 directly or 18. Subtract 18 from 40 and get 22, which is the same thing.

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