Algebra isosceles triangle and square

Question

An isosceles triangle and a square have the same perimeter. The square has an area of 36x². Find the side lengths of the triangle (base = 2x) (one side = 3x+1)

Answer 1

side of the square = sqr(36x^2) = 6x

perimeter of the square = 4(6x) = 24x = sum of 3 sides of the triangle = 2(3x+1)+2x = 8x+2

24 x = 8x +2

16x = 2

x = 1/8

2x = 2(1/8) = 1/4 = base side

3x+1 = 3(1/8)+1 = 3/8 + 1 = 11/8 for the other two sides of the triangle

2(11/8) + 1/4 = 124 = 3 = triangle's perimeter

square's perimeter = 24(1/8 = 3

triangle dimensions are 1/4 by 1 3/8 by 1 3/8

or 0.25 by 1.375 by 1.375