SOLUTION: ladder is resting against the wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6ft more tahn its distance from the

Question 325877: ladder is resting against the wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6ft more tahn its distance from the wall.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
the ladder , ground and the wall form a right triangle.
The ladder is the hypotenuse of the triangle.
leg1 xfeet ( distance from the wall)
leg2= 18feet
hyp= x+6 feet( length of ladder)
..
x^2+18^= (x+6)^2
x^2+324= x^2+12x+36
x^2-x^2-12x=-324+36
-12x=-288
x=-288/-12
x=24 distance from the wall.
Length of ladder = 24+6 = 30 feet
..
CHECK
18^2+24^2= 30^2
900 = 900

The length of ladder feet 30 feet
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!
ladder is resting against the wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6ft more tahn its distance from the wall.

The ladder resting against the wall forms its length which is also the hypotenuse of a right triangle. This is what is being asked for.

Let the ladder's distance from the wall be D. Since the length of the ladder is 6 ft more than the ladder's distance from the wall, then the ladder's length is D + 6

We now have 2 legs and the hypotenuse of the right triangle. Based on the pythagorean formula, , we will have:

12D = 288
= 24 ft

This means that the hypotenuse or length of the ladder is ft (24 + 6).
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