Geometry Tree shadow

[Layo]

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?

[shankar.ashwin]

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

[rijul007]

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..

[Layo]

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

[neelgandham]

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) ∠DAE = ∠BAC ; ∠DEA = ∠BCA = 90. Since two angles of the triangle AED are equal to two angles of the triangle ACB, ∠CBA = ∠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

[rijul007]

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

[bpdulog]

D

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