In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l

Question

NJNJ.jpg In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the length of ST ? A. 6 B. 12 C. 24 D. 36 E. 72

ScottTargetTestPrep · Accepted Answer

Solution: Although triangle RST looks like a right triangle, we know it is not because of the given measures of the angles. So let’s redraw the triangle that depicts more of the actual shape of the triangle. triangle.png As we can see, triangle RST is an obtuse triangle with the obtuse angle at R. Now extend RT from R to U such that SU is perpendicular to RU. Now we’ve created two right triangles: SUT and SUR. We see that triangle SUT is a 30-60-90 right triangle and triangle SUR is a 45-45-90 right triangle. Let’s look at triangle SUR first. Since SR, the hypotenuse of triangle SUR, is 6√2, we see that, SU and RU, the legs of triangle SUR must be each 6√2/√2 = 6. Now, let’s look at triangle SUT. Since SU, the shortest leg of triangle SUT, is 6, ST, the hypotenuse of triangle SUT, must be 6 x 2 = 12 (notice that UT = 6 + 6(√3 - 1) = 6 + 6√3 - 6 = 6√3, which is exactly √3 times SU). Answer: B

KanishkM · Answer

IMO B

This means side ST will be the greatest side among all.

SR = 6 \sqrt{2}  = 6*1.414 ~ 9

RT = 6( \sqrt{3}  - 1) ~ 4

No ideally it can be 12, 9+4 > 12 & 5 < 12

priyadabas01 · Answer

The value should be between the sum of the two sides and their difference. So in between 6 and 19. Only 12 fits in this category. Hence option B

Posted from my mobile device

MahmoudFawzy · Answer

6\sqrt {2} = 6*1.4 = 8.4 
 6 (\sqrt {3}-1) = 6*(1.7-1) = 6*0.7 = 4.2

so the range is between 12.6 and 4.2

how come 6 and 19?

MahmoudFawzy · Answer

by extending RT to form the right angle triangle TZS,

ZSR is a 45:45:90 triangle with side ratios of  1:1:\sqrt{2} 
so SZ = 6

and SZT is a 30:60:90 triangle with side ratios of  1:\sqrt{3}:2 
so ST = 12

B

priyadabas01 · Answer

My bad. But we can eliminate 6 as the side opposite to the largest angle is the longest.

stne · Answer

Actually answer is B, we can extend side RT to form a right triangle having angles ,90 45 45. You may want to check out this post. https://gmatclub.com/forum/in-triangle- ... l#p2223923

JHTIPU18 · Answer

(6√2)^2 + 6(√3-1)^2 = x^2
X^2 = 36*2 + 36*2
X^2 = 144
X = 12

Answer is : B

Posted from my mobile device

JHTIPU18 · Answer

Is that ok? I mean the method i follow?

Posted from my mobile device

tejasvkalra · Answer

I did it using a different method
we know that area of a triangle is 1/2absinΘ where Θ is the angle between the sides. Let x be the unknown side
first we find out angle SRT , it equals 135
Next we find the area using the two angles 135 and 30
considering SR and RT 
angle between them is 135 
so area is 1/2* 6√2*6(√3-1)* sin 135 ........(1)

Consdierinf ST and RT
angle between them is 30
so area is 1/2*x* 6(√3-1)..........(2)

equating 1 and 2 we get x = 12

In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l

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 Problem Solving (PS) Questions

In triangle RST, shown above, ∠RTS = 30° and ∠RST = 15°. What is the l

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