This is a very interesting problem. What makes it so interesting is that there's so little actual math to it. The only big Math thing you need to know in order to work with this question is the definition of "perimeter".
"Perimeter" means
"the distance all the way around the edge of something".
The problem GIVES you the length of all the sides of both triangles. To find the perimeter of one triangle, just take the lengths of its three sides and addum up.
The perimeter of the blue one is (7x+7) + (5x-4) + (4x+2) . That's it ! That's the perimeter. Of course, they want you to write it in simplest form, so you have to clean it up. Remove all of the parentheses, add up all the 'x's, and add up all the plain numbers, and you'll have a short, pretty expression.
Then do the same thing for the red one, and get its perimeter.
In part-b, they want you to find the difference between the two perimeters. No problem. Just write (the blue perimeter) minus (the red perimeter), and simplify THAT expression.
Now they want the actual perimeters when 'x' is 3. No big deal. Just take each separate perimeter, write '3' in place of 'x', and find the number that the expression becomes.
Just now, looking at the picture without writing anything down, I got 53 for the blue one and 17 for the red one. I could easily be wrong, so you definitely have to work them out for yourself.
We know that the sandbox is square, and that the area is 160 sq ft. Since A = s^2 for a square, let's work backwards and find s if A = 160 sq ft = s^2.
s^2 = 160 = 16(10). We do this because 16 is the largest perfect square factor of 160.
Then the length of one side of the square is approx. s = 4√10 ft (12.65 ft)
