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What is the area of the equilateral triangle if the base BC = 6?

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What is the area of the equilateral triangle if the base BC = 6?  [#permalink]

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New post 15 Oct 2018, 07:03
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What is the area of the equilateral triangle if the base BC = 6?


(A) \(9 \sqrt{3}\)

(B) \(18 \sqrt{3}\)

(C) \(26 \sqrt{3}\)

(D) \(30 \sqrt{3}\)

(E) \(36 \sqrt{3}\)


Attachment:
triangle (1).jpg
triangle (1).jpg [ 9.13 KiB | Viewed 419 times ]

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Re: What is the area of the equilateral triangle if the base BC = 6?  [#permalink]

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New post 15 Oct 2018, 07:14
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Bunuel wrote:
Image
What is the area of the equilateral triangle if the base BC = 6?


(A) \(9 \sqrt{3}\)

(B) \(18 \sqrt{3}\)

(C) \(26 \sqrt{3}\)

(D) \(30 \sqrt{3}\)

(E) \(36 \sqrt{3}\)


Attachment:
triangle (1).jpg


Useful formula: Area of equilateral triangle = (side²)(√3)/4

In this question, we're told that each side has length 6.

So, area = (6²)(√3)/4
= (36)(√3)/4
= 9√3

Answer: A

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Re: What is the area of the equilateral triangle if the base BC = 6?  [#permalink]

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New post 15 Oct 2018, 07:26
Top Contributor
Bunuel wrote:
Image
What is the area of the equilateral triangle if the base BC = 6?


(A) \(9 \sqrt{3}\)

(B) \(18 \sqrt{3}\)

(C) \(26 \sqrt{3}\)

(D) \(30 \sqrt{3}\)

(E) \(36 \sqrt{3}\)


Attachment:
triangle (1).jpg


A different approach....

IMPORTANT: the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise.
So, we can assume that the above diagram IS drawn to scale.
This means we may be able to solve the question by simply "eyeballing" the diagram.

We know that the area of a triangle = (base)(height)/2

We're told that base (BC) has length 6
So, if BC = 6, what do you ESTIMATE for the height of the triangle?
I'd say the height is 4 or 5.
Let's try something in the middle. Let's say the height = 4.5

Using these values, we get: area ≈ (6)(4.5)/2
≈ 27/2
≈ 13.5

Now let's check our answer choices to see which one is closest to 13.5

ASIDE: By test day, all students should have the following approximations memorized:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

A) 9√3 ≈ 9(1.7) ≈ 15 (pretty close!)
B) 18√3 ≈ 18(1.7) ≈ 30 (not close)
We can stop here since the remaining answer choices will be greater than 30

Since A is the ONLY answer choice that's even close to our estimate of 13.5, we can be quite certain that the correct answer is A

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Re: What is the area of the equilateral triangle if the base BC = 6?   [#permalink] 15 Oct 2018, 07:26
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What is the area of the equilateral triangle if the base BC = 6?

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