Question 1167840
side of triangle is s
perimeter is 3s

so side of square is 0.75 s for perimeter of 3s

The square's area is 0.5625 s^2 and that is 13 more than area of triangle.
the area of an equilateral triangle is (1/2)(s)*(s/2)(sqrt(3)=(1/4)s^2(sqrt(3)

therefore (9/16)s^2-13=sqrt(3)/4 s^2, converting to fractional form
or (9/16)s^2-13=4 sqrt(3)s^2/16
and 9s^2-208=4 sqrt(3)s^2
[9-4 sqrt(3)]s^2=208
2.072 s^2=208
s^2=208/(9-4 sqrt(3))
s=10.02 inches, side of the triangle; side of square is 7.51 inches

Check this.
A square is 56.47 in^2 (I didn't round until the last step)

side of triangle is 10.02 in.
altitude is 5.01*sqrt(3) in=8.68 inches
Area of triangle is 43.47 in^2,

The answer is 10.02 inches for the triangle and 56.47 in^2 for the square