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555-605 Level|   Geometry|      
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Bunuel
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Is the area of equilateral triangle A greater than the area of square 29 Jan 2020, 01:46
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35% (medium)

Question Stats:

75% (01:41) correct 25% (01:46) wrong based on 67 sessions

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Is the area of equilateral triangle A greater than the area of square B ?

(1) The product of the length of a side of the square and the length of a side of the triangle is 120.

(2) The ratio of the length of a side of the square to the length of a side of the triangle is 5 to 6.
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Is the area of equilateral triangle A greater than the area of square 29 Jan 2020, 03:01
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Bunuel
Is the area of equilateral triangle A greater than the area of square B ?

(1) The product of the length of a side of the square and the length of a side of the triangle is 120.

(2) The ratio of the length of a side of the square to the length of a side of the triangle is 5 to 6.

Solution


Step 1: Analyse Question Stem


    • Let us assume that a side of square B is s and a side of equilateral triangle A is a. then :
    • Area of triangle A \(= \frac{\sqrt{(3)}}{4}*a^2\)
    • Area of square B = \(s^2\)
    We need to find if \( \frac{\sqrt{3}}{4}*a^2 >s^2\)
        o Or \(\frac{a^2}{s^2 }>\frac{4}{\sqrt{3}}\)
        o Or, \(\frac{a^2}{s^2 }>2.3\)
        Thus, we need to know either the value of a and s or the ratio a:s, then we can find \(\frac{a^2}{s^2} \)and hence figure out which area is greater.

      Step 2: Analyse Statements Independently


      Statement 1: The product of the length of a side of the square and the length of a side of the triangle is 120.
        •According to this statement ,\( s*a=120\)
      From this statement alone, we can not find the value of s and a or the value of \(\frac{a}{s}\).
      Hence, statement 1 is not sufficient and we can eliminate answer options A and D
      Statement 2: The ratio of the length of a side of the square to the length of a side of the triangle is 5 to 6.
        • According to this statement, \(\frac{s}{a} =\frac{5}{6}\)
            o \(\frac{a}{s}=\frac{6}{5}\)
          Since we know \(\frac{a}{s }\), so, we can easily find \(\frac{a^2}{s^2} \) and tell whether area of A is greater than area of B or not.
          Hence statement 2 is sufficient.
          Thus, the correct answer is Option B.
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          Bunuel
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