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?

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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(39616) About Me  (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 a%5E2%2B6%5E2=12%5E2. You can solve for a.
-
sqrt%289%2A12%29
sqrt%283%2A3%2A3%2A2%2A2%29
highlight_green%28a=6%2Asqrt%283%29%29


The equilateral triangle's area:
2%281%2F2%2912%2Aa
or
highlight_green%2812a%29

Answer by MathTherapy(10551) About Me  (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 a%5E2%2B6%5E2=12%5E2, 2%281%2F2%2912%2Aa or highlight_green%2812a%29  WILL NOT get you the equilateral triangle's correct area, as the other person claims.

Correct area: highlight_green%28matrix%281%2C3%2C+36sqrt%283%29%2C+squared%2C+units%29%29