Question

A square with a side length of x+6 has the same perimeter as an equilateral triangle with a side length of 4 x what is the area of the square

Answer 1

The perimeter of the equilateral triangle is 3s and s=4x so the perimeter is:

12x

And we are told that the perimeter of the square is the same.  And that perimeter is 4s where s=(x+6) so that perimeter is equal to

4x+24, and again, we are told that these two values are equal so we can solve for x...

12x=4x+24

8x=24

x=3 and if x=3 then the side length is (x+6)=9

So the area of the square is always A=s^2 and s=9 thus:

A=9^2

A=81 u^2