Question 986224: A square and an equilateral triangle have equal perimeters. The area of the triangle is 163 square centimeters. How long, in centimeters, is a diagonal of the square? Express your answer in simplest radical form.
Thank you
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Triangle, side length s.
Altitude cuts triangle into two special 30 60 90 triangles.
A, the area of The equilateral triangle,
A/2, area of one of the special triangles.
a, altitude of the triangle.
 , one-half base times height, twice
substitute for a,
Solve for s
The SQUARE
Let x be the edge of square shape.
because perimeter of square is given as equal to perimeter of the equilateral triangle.
The diagonal of the square is d.
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Substitute for x to get better formula for d.
Substitute for s to get yet a better formula for d.
Rationalize the expression, the denominator...
and remember, given A=163....
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