Good question from geometry. Level of difficulty: Hard

1. Geometry

2. Geometry
There is an equilateral triangle with a square inscribed inside it. One
of the sides of the square lies on a side of the equilateral . What is
the ratio of the area of the square to that of the equilateral triangle?
(a) 12 : 12 + 7 3 (b) 24 : 24 + 7 3
(c) 18 : 12 + 15 3 (d) 6 : 6 + 5 3

3. Geometry
APQ is an equilateral . As PQ is parallel to BC.
Let side of the square be ‘a’
AP = a = AQ
QRC has angles 30 – 60 – 90.
QR
QC
=
3
2
QC = QR x
2
3
There is an equilateral triangle with a square inscribed inside it. One
of the sides of the square lies on a side of the equilateral . What is
the ratio of the area of the square to that of the equilateral triangle?

4. Geometry
AC = AQ + QC
a +
2a
3
Area of equilateral 
3
4
AC2
3
4
a+
2a
3
2
There is an equilateral triangle with a square inscribed inside it. One
of the sides of the square lies on a side of the equilateral . What is
the ratio of the area of the square to that of the equilateral triangle?

5. Geometry
3
4
3a + 2a
3
2
3
4
x
1
3
a2 (4 + 3 + 4 3)
3a2 7 + 4 3
12
a2 12 + 7 3
12
There is an equilateral triangle with a square inscribed inside it. One
of the sides of the square lies on a side of the equilateral . What is
the ratio of the area of the square to that of the equilateral triangle?

6. Geometry
Ratio of area of square to that of equilateral
 is =
a2
a2 12 + 7 3
12
=
12
12 + 7 3
Answer choice (a)
There is an equilateral triangle with a square inscribed inside it. One
of the sides of the square lies on a side of the equilateral . What is
the ratio of the area of the square to that of the equilateral triangle?

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