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# In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is

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In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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23 Feb 2015, 02:28
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In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:

gsdsq_img1.png [ 9.4 KiB | Viewed 1830 times ]
[Reveal] Spoiler: OA

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In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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23 Feb 2015, 02:54
1
KUDOS
OA must be D.
Triangles above are similar triangle. Since corresponding angles are equal:
A = F = 50
B=G=20
C= H =110
option A is sufficient since ratio of area is given, we can find the ratio of sides from this.
option B also sufficient, since one side in the ratio is provided.
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Last edited by aniteshgmat1101 on 24 Feb 2015, 20:42, edited 1 time in total.

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Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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23 Feb 2015, 03:14

As both are similar Trianges If we know HF we can get FG

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Math Expert
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Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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02 Mar 2015, 05:53
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Bunuel wrote:

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png

MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

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Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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02 Mar 2015, 07:05
Bunuel wrote:
Bunuel wrote:

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png

MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

How do we know that the factor is 3 based off the area being 9 times greater? I'm having trouble making this connection without picking random values for the height of the triangle. On that note, is it possible to solve for the height? Using GMAT tested properties.

Posted from my mobile device

Kudos [?]: 37 [0], given: 30

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139437 [0], given: 12790

Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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02 Mar 2015, 07:10
ak1802 wrote:
Bunuel wrote:
Bunuel wrote:

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Ttriangle FGH has 9 times the area of triangle ABC
(2) HF = 9

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
gsdsq_img1.png

MAGOOSH OFFICIAL SOLUTION:

The information given implies that ∠C = 110° and ∠G = 20°, because the sum of the three angles in each triangle must be 180°, by Euclid’s well-known theorem. Thus, the two triangles have all the same angles, but they are different sizes — they are similar. We know the length of AB, so all we need is the scale factor to determine length of the corresponding side FG.

Statement #1: this statement tells us the ratio of areas is 9 —- this is the square of the scale factor, so k = 3, and from this we can calculate the length of FG. Statement #1, alone and by itself, is sufficient.

Statement #2: this statement gives us a third side, so we can set up a proportion:

AC/AB = FH/FG.

Since we now know three of the terms of that proportion, we can solve for the fourth, FG. Statement #2, alone and by itself, is sufficient.

How do we know that the factor is 3 based off the area being 9 times greater? I'm having trouble making this connection without picking random values for the height of the triangle. On that note, is it possible to solve for the height? Using GMAT tested properties.

Posted from my mobile device

If two similar triangles have sides in the ratio $$\frac{x}{y}$$, then their areas are in the ratio $$\frac{x^2}{y^2}$$.

OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: $$\frac{AREA}{area}=\frac{SIDE^2}{side^2}$$.
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Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is [#permalink]

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17 Sep 2017, 02:36
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Re: In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is   [#permalink] 17 Sep 2017, 02:36
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