SOLUTION: Could you please help me with the following problem? 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

Question 88849: Could you please help me with the following problem? 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.
Thank you very much for any help you can provide.
Answer by malakumar_kos@yahoo.com(315) (Show Source): You can put this solution on YOUR website!

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
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