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

Question

https://gmatclub.com/forum/download/file.php?id=25630 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 . gsdsq_img1.png

aniteshgmat1101 · Answer

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.

RAHULSAINI · Answer

Answer must be B

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

Bunuel · Answer

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.

Answer = D

ak1802 · Answer

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

Bunuel · Answer

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} .

ravigupta2912 · Answer

Can anyone clarify how do they arrive at the fact that the given triangles are similar? I only see 1 angle that is same and we should have information about another angle or about the ratio of two other sides.

CEdward · Answer

We can deduce it from the information given.

∠A = 50° ∠B = 20° ---> ∠C = 110
∠F = 50 ∠H = 110° ---> ∠G = 20

Kaur92 · Answer

Should we assume the length of the sides because of the labels? It aren't stated in the question or the question doesn't anything about the labelling.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards