SOLUTION: A wire is bent into a square enclosing an Area of 48cm^2. If it is to be reshaped as an equilateral triangle, how much araea will be lost?

Question 924758: A wire is bent into a square enclosing an Area of 48cm^2. If it is to be reshaped as an equilateral triangle, how much araea will be lost?
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
is the perimeter, or the length of the wire.

, the wire length.

The equilateral triangle formed with that length of wire is of side length and base length . This is also then the hypotenuse of a special 30-60-90 triangle. You can consider to be the short leg of a 30-60-90 triangle; The height of the equilateral triangle, being the other leg of the special 30-60-90, can be called y.

This y is found, using Pythagorean Theorem, . Find the area of the equilateral triangle from base and height y.

Continuing for y,

The area OF the equilateral triangle here is
, which is half of base*times*height.
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The question asks for the difference or how much area is lost in forming the triangle, so you want to find .
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