Question 1167529
let H = the height of the ladder.
let S = the length of each step.


the height of the ladder is 6 feet longer than the length of each step.


equation for that is H = S + 6


the ladder has 2 pieces of wood that are as long as the height of the ladder and 6 pieces of wood that are as long as the length of each step.


the total amount of wood is 20 feet.


therefore:


2H + 6S = 20


since H = S + 6, then:


2 * (S + 6) + 6S  = 20


simplify to get 2S + 12 + 6S = 20


combine like terms to get 8S + 12 = 20


subtract 12 from both sides of the equation to get 8S = 8


solve for S to get S = 1


the length of each step is equal to 1 foot.


the height of the ladder is S + 6 = 7 feet.


there are 2 pieces of wood that are 7 feet long  each and 6 pieces of wood that are 1 foot long each.


total amount of wood = 2 * 7 + 6 * 1 = 14 + 6 = 20.


the dimensions of the ladder are 7 feet high by 1 foot wide.