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Is the area of equilateral triangle E less than the area of square C ?

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Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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New post 05 Jun 2016, 14:19
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Is the area of equilateral triangle E less than the area of square C ?

(1) A side of square C is \(\frac{2}{3}\) the length of a side of triangle E.

(2) The sum of the perimeters of triangle E and square C is 17

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Re: Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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New post 06 Jun 2016, 03:59
Let 'l' be the length of square and 'a' be the length of equilateral triangle

St1: l = (2/3)*a
Area of equilateral triangle = (\(\sqrt{3}\)/4)*a^2 ----- (1)

Area of square = (4/9)*a^2 ----- (2)

(1)/(2) = Area of eqt. triangle/Area of square = (9*\(\sqrt{3}\))/16 = 9*(1.7)/16 = 15.3/16
Area of equilateral triangle = 0.9 * Area of square
Hence Area of equilateral triangle < Area of square
Sufficient

St2: Perimeter of triangle + Perimeter of square = 17
3a + 4l = 17 --> We have two unknowns.
If a = 1/3 and l = 4 then Area of square > Area of eqt. triangle
If l = 1/2 and a = 5 then Area of eqt. triangle > Area of square
Not Sufficient

Answer: A
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Re: Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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New post 23 Feb 2018, 02:30
AbdurRakib wrote:
Is the area of equilateral triangle E less than the area of square C ?

(1) A side of square C is \(\frac{2}{3}\) the length of a side of triangle E.

(2) The sum of the perimeters of triangle E and square C is 17



square's side 2/3of the equilateral triangles side

unique value obtained

ex - side of square = 2 side of triangle = 3

area of square = 4

area of equilateral triangle = rt3 /4 x 3 x 3 on calculation we can know the value

sufficient


(2) perimeter = 17

multiple solutions for perimeter possible

4a +3b = 17

no unique ans

(A) imo
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Is the area of equilateral triangle E less than the area of square C ?  [#permalink]

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New post 23 Feb 2018, 16:26
If we name one side of the square c and one side of the triangle e, the square's area will be \(c^2\) and equilateral triangle's area will be \(e^2 \sqrt{3}/4\) We need to know whether the area of equilateral triangle E is less than the area of square C .

(1) A side of square C is 2/3 the length of a side of triangle E.

As we know the relationship between the sides, we can assign any numbers in this ratio as the sides of the square and triangle in our formulas for the areas of square and triangle and it will show us which one is larger. sufficient.


(2) The sum of the perimeters of triangle E and square C is 17

This statement just shows that 3e+4c=17 so e and c can take various values which would change the areas of square and triangle. Not sufficient

So the answer is A.
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Is the area of equilateral triangle E less than the area of square C ?   [#permalink] 23 Feb 2018, 16:26
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Is the area of equilateral triangle E less than the area of square C ?

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