If an equilateral triangle and a square have the same area then what

Question

Competition Mode Question

If an equilateral triangle and a square have the same area then what is the ratio of the side of the square to the side of the triangle?

(A)  1 : 2

(B)  2 : 3

(C)  \sqrt{3} : 4

(D)  \sqrt {3} : 4

(E)  \sqrt {3} : 2

freedom128 · Answer

area of equilateral triangle with side a = 0.25a^2✓3, while area of a square with side b = b^2

0.25a^2✓3 = b^2
0.25✓3 = (b/a)^2
(3)^0.25 / 2 = (b/a)

Final answer is (E)

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Archit3110 · Answer

given
√3/4 * a^2 = s^2
√3^1/4 /2 = s/a
IMO E

If an equilateral triangle and a square have the same area then what is the ratio of the side of the square to the side of the triangle?

(A) 1:21:2

(B) 2:32:3

(C) 3‾√:43:4

(D) 3‾√4:434:4

(E) 3‾√4:2

unraveled · Answer

If an equilateral triangle and a square have the same area then what is the ratio of the side of the square to the side of the triangle?

(A) 1:2

(B) 2:3

(C)  \sqrt{3} :4

(D)  \sqrt{√3} :4

(E)  \sqrt{√3} :2

Let side of triangle = a, Area =  \frac{√3}{4}a^2 
Side of square = s, Area =  s^2

Now,  s^2  =  \frac{√3}{4}a^2 
 \frac{s}{a} = \frac{\sqrt{√3}}{4}

Answer D.

eakabuah · Answer

If the l is the length of a side of the equilateral triangle and a is the length of a side of the square, 
then Area of the equilateral triangle = 1/2 * l * h, and h=l * √3 / 2
hence Area of the triangle = l^2 * √3 /4 ------(1)
Area of the square = a^2 ----(2)
But the two areas are equal, hence (1)=(2)
l^2 * √3 /4 = a^2
so a = √((l^2 * √3 /4 )) = l * (3)^0.25 /2 -------(3)
a:l =( l * (3)^0.25 /2 )/ l = (3)^0.25 / 2

The answer is E.

ManasviHP · Answer

root (3)/ 4 a^2 = s^2
where a is side an equilateral triangle and s is side of square. Hence, s/a = option E

ScottTargetTestPrep · Answer

Letting s = the length of the side of the square and t = the length of a side of the triangle, we can create the equation:

s^2 = (t^2√3)/4

4s^2 = t^2√3

s^2/t^2 = √3/4

s/t = ∜3/2

Answer: E

Jawad001 · Answer

Let side of equilateral triangle = a and side of the triangle = b
Area of equilateral triangle =√3/4 a^2
Area of the triangle = b^2
b^2 =√3/4 a^2
b =∜3/2 a
the ratio of the side of the square to the side of the triangle = b/a = (∜3/2 a)/a = ∜3/2 = ∜3 ∶2(E)

ostrick5465 · Answer

The length of the edge of the equilateral triangle is: a
=> The area of the equilateral triangle is  a * \frac{a\sqrt{3}}{2} : 2 = \frac{a^{2}\sqrt{3}}{4} 
The length of the edge of the square is: b
=> The area of the square is:  b^{2}

=>  b^{2} =\frac{a^{2}\sqrt{3}}{4} 
=>  \frac{b}{a} = \frac{\sqrt {3} }{ 2} 
=>  Choice E

exc4libur · Answer

area_square:area_equilateral:
a^2=x^2√3/4, x^2=4a^2/√3, x=2a/3^(1/4)

side_square:side_equilateral
a:x, a:2a/3^(1/4), 3^(1/4):2

Ans (E)

If an equilateral triangle and a square have the same area then what

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GMAT Problem Solving (PS) Questions

If an equilateral triangle and a square have the same area then what

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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