# SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista

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 Question 145407: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.Answer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder. : Using the formula a^2 + b^2 = c^2 : Let x = length of the ladder (c) : "The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder." Therefore: (x-3) = a : "the distance of its top to the ground is 4 feet less than the length of the ladder." therefore: (x-4) = b : Using the formula we have: (x-3)^2 + (x-4)^2 = x^2 FOIL (x^2 - 6x + 9) + (x^2 - 8x + 16) = x^2 : Combine like terms on the left x^2 + x^2 - x^2 - 6x - 8x + 9 + 16 = 0 : x^2 - 14x + 25 = 0 : Solve for x using the quadratic formula; a=1; b=-14; c=25 : : you can do the math here, the reasonable solution is x = 11.9' length of ladder : : Check solution 8.9^2 + 7.9^2 = 141.6 which is 11.9 squared