GMAT Problem Solving - Triangle Geometry

[ravis25]

In the Figure Above, what is the value of X?

A) 50
B) 60
C) 65
D) 70
E) 75

[sk818020]

IMO the answer is D.

3:4:5 and 5:12:13 are common right triangles. You can use this to conclude that two sides of the middle triangle are 5 and 5. Thus, the triangle is isosceles and the two bottom angles must both be 55 degrees and the top angle must be 70 (180-55-55=70).

You could use Pythagorean theorem to figure figure the two sides out, but it is often recommended that you memorize those common ratios of right triangles.

Hope that helps.

Thanks,

Jared

[ravis25]

IMO the answer is D.

3:4:5 and 5:12:13 are common 30-60-90 right triangles. You can use this to conclude that two sides of the middle triangle are 5 and 5. Thus, the triangle is equilateral and the two bottom angles must both be 55 degrees and the top angle must be 70 (180-55-55=70).

You could use Pythagorean theorem to figure figure the two sides out, but it is often recommended that you memorize those common ratios of right triangles.

Hope that helps.

Thanks,

Jared

awesome that helps.....looks like i was not counting on the common sides triangles

[4GMAT_Mumbai]

3:4:5 and 5:12:13 are common 30-60-90 right triangles

Hi ... Just a minor correction (Not something which changes the eventual answer)

3,4,5 and 5,12,13 are not 30-60-90 triangles ... they are not in the ratio "1 : root 3 : 2"

These are just pythagorean triplets to be kept in mind.

[sk818020]

3:4:5 and 5:12:13 are common 30-60-90 right triangles

Hi ... Just a minor correction (Not something which changes the eventual answer)

3,4,5 and 5,12,13 are not 30-60-90 triangles ... they are not in the ratio "1 : root 3 : 2"

These are just pythagorean triplets to be kept in mind.

That is correct. Nice catch. Sorry about the mistake if it threw anyone off.

[kvcpk]

The center trialngle shud be isoceles. SO answer shud be x=70
IMO answer is D

[Patrick_GMATFix]

Memorizing the common Pythagorean triples can save a ton of time. A quick look at the 2 right triangles should tell you that we're dealing with a 3-4-5 on the left and a 5-12-13 on the right. Thus the middle triangle is Isoceles with two fives equal to 5.

In any triangle, if 2 sides are equal, their facing angles must be equal; thus the two base angles of the middle triangle must equal each other and equal 55.

In any triangle, the sum of angles is 180. In the middle triangles, the known angles add up to 55+55=110. Since x is the missing angle, we can write 110+x=180 --> x = 70. The answer is D.

A video solution with detailed explanation is available at GMATPrep question 1190. With the Drill Engine, you can generate timed drills of similar questions by setting topic='Geometry' and difficulty='500-600'.

Good luck,
-Patrick

[pradeepkaushal9518]

u have to remember the sides of right angle triangles 3,4,5 and 5,13,12 so the triangle become isoceles triangle so 180-55-55=70