Question 343301
The top of a 15ft ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?


Let the distance from the bottom of the wall to the bottom of the ladder be B


Since the top of the ladder is 3ft farther up the wall than the foot of the ladder is from the base of the wall, then the ladder is (B + 3) ft up the wall


Using pythagorean, we get {{{B^2 + (B + 3)^2 = 15^2}}}

{{{B^2 + B^2 + 6B + 9 = 225}}}

{{{2B^2 + 6B - 216 = 0}}}

{{{2(B^2 + 3B - 108) = 2(0)}}}

{{{B^2 + 3B - 108 = 0}}}

(B + 12)(B - 9) = 0_____Factoring equation

B + 12 = 0   OR  B  -  9  = 0


B = - 12 (ignore), or B = 9


Therefore, B, or the distance from the bottom of the ladder to the base of the wall is: {{{highlight_green(8)}}} feet.