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If the perimeter of an equilateral triangle is P, what is the altitude

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
If the perimeter of an equilateral triangle is P, what is the altitude  [#permalink]

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08 Mar 2019, 02:21
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Difficulty:

35% (medium)

Question Stats:

78% (01:31) correct 22% (02:13) wrong based on 41 sessions

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If the perimeter of an equilateral triangle is P, what is the altitude of the triangle in terms of P?

A. p/6

B. p/3

C. $$\frac{p\sqrt{3}}{2}$$

D. $$p\sqrt{3}$$

E. $$\frac{p\sqrt{3}}{6}$$

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Joined: 04 Jan 2015
Posts: 3074
Re: If the perimeter of an equilateral triangle is P, what is the altitude  [#permalink]

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08 Mar 2019, 02:38

Solution

Given:
• Perimeter of an equilateral triangle = P

To find:
• The altitude of the triangle, in terms of P

Approach and Working:
As the perimeter of the equilateral triangle is P,
• Length of each side = $$\frac{P}{3}$$
• Therefore, length of the altitude = $$\frac{√3}{2} * \frac{P}{3} = \frac{P√3}{6}$$

Hence, the correct answer is option E.

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Location: India
Concentration: Sustainability, Marketing
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Re: If the perimeter of an equilateral triangle is P, what is the altitude  [#permalink]

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08 Mar 2019, 04:08
Bunuel wrote:
If the perimeter of an equilateral triangle is P, what is the altitude of the triangle in terms of P?

A. p/6

B. p/3

C. $$\frac{p\sqrt{3}}{2}$$

D. $$p\sqrt{3}$$

E. $$\frac{p\sqrt{3}}{6}$$

height of equilaterla triangele ' √3 * side / 2
so here side = P /3
so height = $$\frac{p\sqrt{3}}{6}$$
IMO E
Senior Manager
Joined: 12 Sep 2017
Posts: 301
If the perimeter of an equilateral triangle is P, what is the altitude  [#permalink]

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12 May 2019, 17:47
EgmatQuantExpert wrote:

Solution

Given:
• Perimeter of an equilateral triangle = P

To find:
• The altitude of the triangle, in terms of P

Approach and Working:
As the perimeter of the equilateral triangle is P,
• Length of each side = $$\frac{P}{3}$$
Therefore, length of the altitude = $$\frac{√3}{2} * \frac{P}{3} = \frac{P√3}{6}$$

Hence, the correct answer is option E.

Hello EgmatQuantExpert!!!

Is the red part a formula?

Kind regards!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: If the perimeter of an equilateral triangle is P, what is the altitude  [#permalink]

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13 May 2019, 11:36
jfranciscocuencag wrote:
EgmatQuantExpert wrote:

Solution

Given:
• Perimeter of an equilateral triangle = P

To find:
• The altitude of the triangle, in terms of P

Approach and Working:
As the perimeter of the equilateral triangle is P,
• Length of each side = $$\frac{P}{3}$$
Therefore, length of the altitude = $$\frac{√3}{2} * \frac{P}{3} = \frac{P√3}{6}$$

Hence, the correct answer is option E.

Hello EgmatQuantExpert!!!

Is the red part a formula?

Kind regards!

Hey jfranciscocuencag,
Yes it is a formula for an equilateral triangle.
If the length of each side of an equilateral triangle is a, then

Height (or Altitude) of the triangle = $$\frac{√3}{2} * a$$
Area of the triangle = $$\frac{√3}{4} * a^2$$
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Re: If the perimeter of an equilateral triangle is P, what is the altitude   [#permalink] 13 May 2019, 11:36
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