Solve.
-A ladder is resting against a 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 6 ft more than its distance from the wall.
A)36 ft
B)24 ft
C)30 ft
D)18 ft

Question

Quizplus · Accepted Answer

Let x be the distance between the wall and the foot of the ladder. According to the problem, we have:
ladder length = x + 6 (as the length is 6 ft more than its distance from the wall)
ladder height = 18 ft
By applying the Pythagorean Theorem, we obtain:
(x+6)^2 + 18^2 = (ladder length)^2 = (x+6)^2 + 18^2
Simplifying this equation, we get:
x^2 + 12x - 360 = 0
Solving this quadratic equation, we get:
x = 18 or x = -30
Since x cannot be negative, we have x = 18. Therefore, the length of the ladder is:
ladder length = x + 6 = 18 + 6 = 24 ft.
So, the answer is choice C. Let's call the distance from the wall "x". According to the problem, the length of the ladder is "6 feet more than its distance from the wall", or x+6. We can use the Pythagorean theorem to set up an equation: 
x² + 18² = (x+6)² 
x² + 324 = x² + 12x + 36 
288 = 12x 
x = 24

So the distance from the wall is 24 feet, and the length of the ladder is x+6, or 30 feet. Therefore, the answer is choice C.

Solve. -A Ladder Is Resting Against a Wall. the Top of of the Ladder