Question 1005225
this forms a triangle.


the ladder is the hypotenuse of the triangle with a length of 13.


the base of the triangle is equal to x, or any other variable name you want to use.


the height of the triangle is equal to 2x + 2.


this represent 2 more than twice the distance from the wall to the ladder.


use pythagorus to find the value of x.


pythagorus says:


a^2 + b^2 = c^2


set a = x


set b = 2x + 2


set c = 13


you get:


a^2 + b^2 = c^2 becomes:


x^2 + (2x+2)^2 = 13^2


simplify to get x^2 + 4x^2 + 4x + 4x + 4 = 169


simplify further to get x^2 + 4x^2 + 8x + 4 = 169


combine like terms to get 5x^2 + 8x + 4 = 169


subtract 169 from both sides of the equation to get 5x^2 + 8x - 165 = 0


factor this quadratic any way you can and you will get:


(5x + 33) * (x - 5) = 0


solve for x and you will get:


x = -33/5 and x = 5


since x has to be greater than 0, your solution is x = 5.


the distance from the wall to the base of the ladder is 5 feet.


the distance from the top of the ladder to the ground is 2*5+2 = 12 feet.


since 12^2 + 5^2 = 13^2, the measurements look good.