Question 88849

 A 15 foot ladder is leaning against a building. The bottom of the ladder is distance d from the building and the top of the ladder is d + 3 ft up the building. Find these lengths

  Let ABC represent the sides of a right angle triangle such that 
    AB = height of the building above the ground at which ladder touches = d+3
    BC = the length of the ladder  = 15 ft
    AC = the distance of the  bottom of ladder from the building = d ft
    The triangle is such that angle A = 90 degrees . so hypotenuse will be BC
     Apply pythagorous theorem  ,  BC^2 = AB^2+AC^2
                                   (15)^2 = (d+3)^2+(d)^2
                                      225 = d^2+6d+9+d^2
                                      225-9 = 2d^2=6d
                                     2d^2+6d-216 = 0
                                     2d^2+24d-18d-216=0
                                     2d(d+12)-18(d+12) = 0
                                     (d+12)(2d-18) = 0
               if 2d-18 = 0 then d = 18/2 = 9 then d+3 = 9+3 = 12
                if d+12 = 0 then d = -12     hence d+3 = -12+3 = -9

      The distance of the bottom of the ladder from the building = 9 ft
      the height at which the ladder is touching the building  = 12 ft