SOLUTION: A square and an equilateral triangle have equal perimeters. The area of the triangle is {{{16sqrt(3) cm^2}}}. How long, in centimeters, is a diagonal of the square? Express your an

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A square and an equilateral triangle have equal perimeters. The area of the triangle is {{{16sqrt(3) cm^2}}}. How long, in centimeters, is a diagonal of the square? Express your an      Log On

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Question 261724: A square and an equilateral triangle have equal perimeters. The area of the triangle is 16sqrt%283%29+cm%5E2. How long, in centimeters, is a diagonal of the square? Express your answer in simplest radical form.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/2 bh=16sqrt%283%29
1%2F2%2A8%2A4sqrt%283%29=32sqrt%283%29
each side is 8
triangle perimeter 24
square perimeter 24
each side 2sqrt%286%29
d^2=2*24=48
d=sqrt%2848%29=sqrt%284%2A4%2A3%29=4sqrt%283%29