SOLUTION: http://img.geocaching.com/cache/large/8f671ade-1846-4e62-b2d7-2c73512ae1c8.gif Three big one-inch squares (S3) are joined corner-to-corner to make an equilateral triangle. Insid

Question 620349: http://img.geocaching.com/cache/large/8f671ade-1846-4e62-b2d7-2c73512ae1c8.gif
Three big one-inch squares (S3) are joined corner-to-corner to make an equilateral triangle. Inside that triangle, three little squares (S1) are fit into a similar shape. Finally, the line segment from the little square to the corner of the large triangle is used to form the medium square (S2) as shown.
-----(SEE IMAGE)-----
What is the ratio of areas of the medium square to the little square (S2:S1)?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I see three little kites in the corners of the triangle.
If you split one of them along the long diagonal, you get two congruent 30-60-90 right triangles.
The ratio of short leg to long leg in those triangles (and in all 30-60-90 right triangles) is .
(It is usually written as just for elegance, but it works better for me as in this case).
That is the ratio of the side of the small square to the side of the medium square.
The ratio of their areas is the square of the ratio of their sides, or .
RELATED QUESTIONS
Identify the lines that are perpendicular: LINES:... (answered by MathLover1)

Perform the indicated operation and expression lowest terms. Thanks for any help. (answered by CubeyThePenguin)
Perform the indicated operation and expression lowest terms. (answered by CubeyThePenguin)
Find the value of x that makes the following equation true: (answered by math_tutor2020,MathTherapy)
QUESTION: http://my.thinkwell.com/questionbank/95001-96000/95629/img/242045.gif GRAPH: (answered by josgarithmetic)
Identify the sides of ΔMNO in order from shortest to longest.... (answered by MathLover1)
The equations of four lines are given. Identify which lines are parallel. LINES:... (answered by Fombitz)
Help please 1. Which of the following shows that ΔPQS ≅ ΔRQS, when... (answered by MathLover1)
Given that A(0, 0), B(4, 0), C(0, 2), D(0, 0), E(12, 0), and F(0, 6), which of the... (answered by Fombitz,MathLover1)