SOLUTION: A square whose area is 81 has its perimeter equal to the perimeter of an equilateral triangle. What is the area of the triangle?

Question 1185239: A square whose area is 81 has its perimeter
equal to the perimeter of an equilateral
triangle. What is the area of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The dimensions of any side of the given square is 9 units. Perimeter of this given square is 36 units.

Equilateral triangle with that same 36 unit perimeter, each side of this triangle is 12 units.

Area for this triangle:
This can be cut into two right triangles with hypotenuse 12, short leg 6, and longer leg a, so that . You can solve for a.
-

The equilateral triangle's area:

or

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!
A square whose area is 81 has its perimeter
equal to the perimeter of an equilateral
triangle. What is the area of the triangle?

With , or WILL NOT get you the equilateral triangle's correct area, as the other person claims.
Correct area:
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