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What is the length of line segment AB in the figure above?

This topic has 2 expert replies and 1 member reply

What is the length of line segment AB in the figure above?

Post Sun Dec 03, 2017 1:22 pm


What is the length of line segment AB in the figure above?

A. (√2)/2
B. (√3)/2
C. √2
D. 3/2
E. √3

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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Post Fri Jan 12, 2018 6:40 am
LUANDATO wrote:


What is the length of line segment AB in the figure above?

A. (√2)/2
B. (√3)/2
C. √2
D. 3/2
E. √3
If we drop a perpendicular from vertex A to side BC, that is, if we draw the height, we will divide the triangle into two special right triangles: a 45-45-90 triangle on the left and a 30-60-90 triangle on the right. Let’s call this height AD, that is, D is a point on BC such that AD is perpendicular to BC.

We know that the side ratio of a 45-45-90 triangle is x : x : x√2. Since AC = 1, we see that if we let AD = x, then x√2 = 1. So x = 1/√2 = √2/2 = AD.

We also know that the side ratio of a 30-60-90 triangle is x : x√3 : 2x. Since AD = √2/2, we see that AB must be twice as much. So AB = 2(√2/2) = √2.

Answer: C

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Post Mon Dec 04, 2017 7:55 pm
LUANDATO wrote:


What is the length of line segment AB in the figure above?

A. (√2)/2
B. (√3)/2
C. √2
D. 3/2
E. √3

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Use the following formula

a/sinA = b/sinB = c/sinC
where a,b and c are the lengths of the sides of the triangle and A, B and C are the opposite angles.

Based on this,

AC/sin30 = AB/sin45

1/(1/2) = AB/(1/ √2)

Or AB = 2/√2

Or AB = √2

Let me know if this makes sense.

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GMAT/MBA Expert

Post Sun Dec 03, 2017 7:12 pm
Hi LUANDATO,

I'm going to give you some hints so that you can reattempt this question on your own:

1) The GMAT sometimes "hides" special right triangles (30/60/90, 45/45/90, 3/4/5, 5/12/13) inside of other shapes, so when a prompt includes an uncommon shape, you might try breaking the shape down into 'pieces.'
2) In this question, try cutting the triangle into 2 pieces (draw a line from point A down to the base). You'll form 2 triangles. What do you know about those triangles?
3) With the one side length that you're given, you should be able to fill in all of the other side lengths (although you don't technically have to do all of that work to answer the question that is asked).

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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