SOLUTION: the foot of a ladder is 9 feet from the wall. the ladder is 3 feet longer than the distance it reaches up the wall. How far up the wall does the ladder reach?

Question 369111: the foot of a ladder is 9 feet from the wall. the ladder is 3 feet longer than the distance it reaches up the wall. How far up the wall does the ladder reach?
Found 2 solutions by neatmath, ewatrrr:
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!
We will certainly use the Pythagorean Theorem on this one, as expected.

Let h be the height of the wall, or the height of the wall where the top of the ladder touches.

Let w be the width of the ground, or the width of the ground where the bottom (foot) of the ladder touches.

Let l be the length of the ladder itself.

We are given w=9 feet

We are also given that h+3=l

Now we should be able to set up the Pythagorean Theorem:

or in this case:

substituting all known values

Therefore, the top of the ladder should reach up to 12 feet on the wall.

Also, now that we know how far the ladder reaches up (12 feet) and how far the ladder reaches away from the wall (9 feet), we can now find out how long the ladder actually is!

Therefore the ladder is 15 feet long. You didn't need to know that solve the problem, but it's certainly nice to get the complete picture.

I hope this helps!

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Let x represent the length up the wall. Then ladder length would be (x+3)
applying the Pythagorean Theorem
9^2 + x^2 = (x+3)^2
81 + x^2 = x^2 + 6x + 9
72 = 6x
12 = x, length up the wall the ladder reaches
checkingour answer
81 + 144 = 225 = 15^2
RELATED QUESTIONS
The foot of an extension ladder is 10 feet away from the base of a wall. The ladder is 2... (answered by checkley79,scott8148)
The foot of an extension ladder is 15 ft from a wall. The ladder is 5 ft longer than the (answered by Fombitz)
A 25-foot ladder is placed so that it reaches to a point on the wall that is 3 feet... (answered by mananth)
A fifteen foot long ladder is leaned against a wall so that the distance it reaches up... (answered by josgarithmetic)
A -foot ladder is placed so that it reaches to a point on the wall that is feet higher... (answered by oberobic)
13 -foot ladder is placed so that it reaches to a point on the wall that is 2 feet... (answered by josgarithmetic)
A -foot ladder is placed so that it reaches to a point on the wall that is feet higher... (answered by oberobic)
A 25-foot ladder is placed so that it reaches to a point on the wall that is 5 feet... (answered by macston)
a ladder is resting against a wall. the top of the ladder touches the wall at height of... (answered by mananth)