A 13-foot ladder is placed so that it reaches to a point on the wall that is 2 feet higher than twice the distance from the base of the wall to the base of the ladder. How high does the ladder reach?

Question

Quizplus · Accepted Answer

Let x be the distance from the base of the wall to the base of the ladder. Then, according to the problem, the height that the ladder reaches is 2x + 2 feet. We can use the Pythagorean theorem to set up an equation:

x^2 + (2x + 2)^2 = 13^2

Expanding and simplifying, we get:

5x^2 + 8x - 135 = 0

Factorizing, we get:

(5x - 27)(x + 5) = 0

Since x cannot be negative, we have:

x = 27/5

Therefore, the height that the ladder reaches is:

2x + 2 = 56/5

Simplifying, we get:

11 1/5 feet

which is closest to answer choice B, 12 feet.

A 13-Foot Ladder Is Placed So That It Reaches to a Point