A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jevonte grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 45 ft.) Round to the nearest tenth of a foot.
Let x be the distance the ladder moves along the house.
Using the Pythagorean theorem, we have:
(48 + x)^2 = 52^2
2304 + 96x + x^2 = 2704
x^2 + 96x - 400 = 0
Using the quadratic formula, we get:
x = (-96 ± √(96^2 + 1600))/2
x = (-96 ± √(9216 + 1600))/2
x = (-96 ± √10816)/2
x = (-96 ± 104)/2
x = (-96 + 104)/2 or x = (-96 - 104)/2
x = 8/2 or x = -200/2
x = 4 or x = -100
Since x = 4 is the only valid solution for this problem, the ladder will reach up 48 + 4 = 52 feet along the side of the house. So the ladder will reach 52 feet up the side of the house now.