Answer:
The side of the triangle is 14 inches.
Step-by-step explanation:
Let the side of triangle be 'x' and square be 'y'.
Given:
Perimeter of triangle is 18 inches more than the perimeter of square.
Side of triangle is 8 inches longer than the side of square.
Perimeter is the sum of all the sides of a given shape.
Perimeter of an equilateral triangle is given as:
Perimeter = 3 × Side length = [tex]3x[/tex]
Perimeter of a square is given as:
Perimeter = 4 × Side length = [tex]4y[/tex]
Now, as per question:
Perimeter of triangle = Perimeter of square + 18
[tex]3x=4y+18[/tex] -------------- (1)
Side of triangle = Side of square + 8
[tex]x=y+8[/tex] ------------------- (2)
Rewriting equation (2) in terms of 'y', we get:
[tex]y=x-8[/tex]
Now, plug in the 'y' value in equation (1) and solve for 'x'. This gives,
[tex]3x=4(x-8)+18\\\\3x=4x-32+18\\\\3x=4x-14\\\\4x-3x=14\\\\x=14[/tex]
Therefore, the side of the triangle is 14 inches.
