SOLUTION: A square has an area of 27 units. If the perimeter of the square is equal to the perimeter if the equilateral triangle, find the area of the equilateral triangle

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Question 772304: A square has an area of 27 units. If the perimeter of the square is equal to the perimeter if the equilateral triangle, find the area of the equilateral triangle
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First main goal is find the side length of the equilateral triangle.

SQUARE: 27=w%5E2 for w being length of side of the square.
w=sqrt%2827%29
w=3%2Asqrt%283%29
Perimeter is then 4%2A3%2Asqrt%283%29
Perimeter is 12%2Asqrt%283%29

Let t = side length of equilateral triangle. Given is the perimeter is the same as that of the square, so, 3t=4w
3t=12%2Asqrt%283%29
t=12%2Asqrt%283%29%2F3
highlight%28t=4%2Asqrt%283%29%29

WHAT WE KNOW ABOUT EQUILATERAL TRIANGLE
The altitude splits the triangle into two congruent right triangles of hypotenuse t and one leg of t/2. The other leg, the altitude of the equilateral triangle, is then some a, a=sqrt(t^2-(t/2)^2);
a=t%2A%28sqrt%283%29%2F2%29

AREA OF EQUILATERAL TRIANGLES:
Base times height then divided by 2;
%281%2F2%29%28t%2F2%29%28a%29
%281%2F2%29%28t%2F2%29%28t%2Asqrt%283%29%2F2%29
t%5E2%28sqrt%283%29%2F8%29

Finally substitute for value of t:
%28%284%2F3%29sqrt%2827%29%29%28sqrt%283%29%2F8%29
%282%5E4%2A3%2A3%2Asqrt%283%29%29%2F%289%2A2%5E3%29
2%2A3%2Asqrt%283%29
highlight%286%2Asqrt%283%29%29___________Final Answer

NOTE: Draw a picture will help.