What is the area of an equilateral triangle that has an altitude of le

Question

What is the area of an equilateral triangle that has an altitude of length 24?

(A)  24 \sqrt{3}

(B)  48 \sqrt{3}

(C)  96 \sqrt{3}

(D)  192 \sqrt{3}

(E)  384 \sqrt{3}

pushpitkc · Answer

An equilateral triangle of side 2 will have an altitude  \sqrt{3} 
(because the altitude of the equilateral triangle will form a 30-60-90 triangle with the base)

Since, the altitude of the equilateral triangle is 24, the side is  \frac{48}{\sqrt{3}}

Formula used:   Area(equilateral triangle) =  \frac{\sqrt{3}}{4} * side^2 
 
Therefore, the area of the equilateral triangle for side  \frac{48}{\sqrt{3}}  is  \frac{\sqrt{3}}{4}*48*\frac{48}{3} = 192 \sqrt{3}   (Option D)

generis · Answer

equi4.26.18.png • An equilateral triangle's altitude always creates creates two 30-60-90 triangles Each vertex = 60° Vertex B is bisected: two 30° angles Vertex C = 60° Point D = two 90° angles A 30-60-90 triangle has corresponding sides opposite those angles in ratio x : x\sqrt{3} : 2x We need to find x = \frac{1}{2} of base • Divide the altitude by \sqrt{3} Altitude BD, opposite the 60° angle, corresponds with x\sqrt{3} x\sqrt{3}=24 x=\frac{24}{\sqrt{3}}=( \frac{24}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}})=\frac{24\sqrt{3}}{3}=8\sqrt{3} x=8\sqrt{3}=\frac{1}{2}b, base* • Area of triangle , A=\frac{1}{2}*b*h A= (8\sqrt{3}* 24)=192\sqrt{3} Answer D * No need to find the whole base. Area is divided by 2. But IF you wanted to: Base = 2x =(2*8\sqrt{3})=16\sqrt{3} Area, A=\frac{b*h}{2} A=\frac{16\sqrt{3}*24}{2}=(8\sqrt{3}*24)=192\sqrt{3}

D3N0 · Answer

Ans: E

In equilateral triangle of side a altitude is given by 3^(1/2) (a/2) so we can get the a from here.
and area is 1/2(altitude* side of the triangle) = which here is  192 \sqrt{3} 
Ans E

ScottTargetTestPrep · Answer

When we drop an altitude in an equilateral triangle we create two 30-60-90 right triangles in which the altitude is opposite the 60 degree angle; thus, the altitude = side√3/2, thus:

side√3/2 = 24

side = 48/√3

We may recall that the area formula for an equilateral triangle is (side^2 * √3)/4, thus:

area =  /4

area = 768√3/4 = 192√3

Alternate Solution:

When we drop a perpendicular (altitude) in an equilateral triangle, we create two 30-60-90 triangles, each with a ratio of sides of x : 2x : x√3. The altitude is x√3, and so we have:
 
x√3 = 24

x = 24/√3

x = (24√3)/3

x = 8√3

We see that 8√3 is the base of one of the 30-60-90 triangles, so the base of the entire equilateral triangle is 16√3.
 
Using the formula for the area of a triangle: A = 1/2 b x h, we have:

A = (1/2) x 16√3 x 24 = 192√3

Answer: D

veerberry123 · Answer

Is knowing the various formulas of equilateral triangles required on the gmat?

What is the area of an equilateral triangle that has an altitude of le

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