SOLUTION: This word problem has me stomped. When a 26 foot ladder is leaned on a house, the distance from the base of the ladder to the house is 14 ft less than the distance from

Question 6315: This word problem has me stomped.
When a 26 foot ladder is leaned on a house, the distance from the base of the ladder to the house is 14 ft less than the distance from the top of the ladder to the ground. How far up the side of the house is the ladder?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
If you were to draw a diagram of this problem, you would see that you have a right triangle in which the ladder is the hypotenuse, the distance from the base of the house is the base, and the distance from the ground to the top of the ladder is the height.
Using a well-known (we hope) theorem due to Pythagorus, in any right triangle:
where c (26 ft.) is the hypotenuse and a (b - 14 ft) and b are the legs.
In this problem, you are looking for b, the height of the right triangle which represents the height of the top of the ladder from the ground.

26^2 = (b - 14)^2 + b^2 Simplify and solve for b.
676 = (b^2 - 28b + 196) + b^2
676 = 2b^2 - 28b + 196 Rewrite into "standard" quadratic equation form.
2b^2 - 28b - 480 = 0 First divide both sides by 2 then solve by factoring.
b^2 - 14b - 240 = 0 Factor.
(b + 10)(b - 24) = 0 Apply the zero products principle.
b+10 = 0; b = -10 Discard this root as the height must be positive.
b - 24 = 0;, b = 24 ft. This is the distance of the top of the ladder from the ground.
You can check this by:
26^2 = (24 - 14)^2 + 24^2
I'll leave this as an exercise for the student.

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