SOLUTION: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9ft. Find the length of the ladder if the length is 3ft more than its distance from the wa

Question 218246: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9ft. Find the length of the ladder if the length is 3ft more than its distance from the wall.

Found 2 solutions by RAY100, drj:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Let d=distance from wall in ft
.
ladder is then (d+3) long in feet
.
We now have a right triangle with legs,,9,,and d,,,,with hypotenuse (d+3)
.
Using the Pythagorean Theorem,,c^2 =a^2 + b^2,,,
.
(d+3)^2 = d^2 +9^2
.
d^2 +6d +9 = d^2 +81
.
6d = 72
.
d=12 ft,,,,ladder is 12+3 = 15 ft
.
checking ,,,,9^2 +12^2 = 81 +144 =225 = 15^2,,,,ok
.
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9ft. Find the length of the ladder if the length is 3ft more than its distance from the wall.

Step 1. Let h=9 be the height the ladder touches the wall.

Step 2. Let d=3 ft be the distance from wall

Step 3. Let L be the length of the ladder and L=3+d since length is 3 ft more than d.

Step 4. We can use the Pythagorean Theorem for a right triangle which states that the sum of the squares of the legs (h and d) is the number of the squares of the hypotenuse or L in this case. That is,

Subtract 9 from both sides of the equation

Divide 6 to both sides of the equation

and

Step 5. ANSWER: The length of the ladder is 15 feet.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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