The side of a triangle with 3 equal sides is 3 inches shorter than the side of a square. The perimeter of the square is 30 inches more than the perimeter of the triangle. Find the length of a side of the square.

Answer:Side of the square is 21 inchesStep-by-step explanation:Look at the attached image where the three equal side triangle is represented with "[tex]a[/tex]" being the length of each of the triangle's sides, and "b" being the length of each of the square's sides.Now let's write the quantities they are asking us to use to set up equations:One is the perimeter of the square (this is the addition of its 4 equal sides) which gives: [tex]b+b+b+b=4b[/tex]The other one is the perimeter of the triangle (this is the addition its three equal sides) which gives [tex]a+a+a= 3a[/tex]Now set the equations to solve:(1) "The side of the triangle is 3 inches shorter than the side of the square"Can be written in algebraic form using the letters that we have assign to represent each side of the figures:[tex]a = b - 3[/tex](2) "The perimeter of the square is 30 inches more than the perimeter of the triangle" Since we know the perimeter of the square equals [tex]4b[/tex] and the perimeter of the triangle [tex]3a[/tex] , this sentence can be written in algebraic form as:[tex]4b =3a + 30[/tex]Now replace the value for the side of the triangle in terms of the side of the square found in the first expression, in the second equation, and solve for the unknown "b":[tex]4b = 3 (b-3)+30\\4b=3b-9+30\\b=-9+30=21[/tex]Therefore, the side "b" of the square is 21 inches.