Question

the length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. the perimeter of the piece of steel is 68 meters. Find the length of the piece of steel. Find the width of the piece of steel.

Answer 1

n= width
3n-2 = length
perimeter = 68m

so  2(n+3n-2) =68               (n+3n-2) = one width and one length - just half way    
                                          around the rectangle - that's why I multiplied the                                                   entire expression by the 2 outside the parentheses.
Now simplify inside the parenthesis and you get
2 (4n-2) = 68
Now multiply and make sure you use the distributive law
8n - 4 = 68
Add 4 to both sides
8n = 72    now divide both sides by 8 and you get n=9
so the width is 9 and the length (3n-2) = 3x9-2 or 25

Check: 2(l+w) = 68 (perimeter)   2(9+25) = 68    2(34) = 68   68=68

So the width is 9 and the length is 25