Answered

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A 5-ft ladder rests against the side of a house. The distance between the top of the ladder and the ground is 1 ft more than the distance between the base of the ladder and the bottom of the house. Find both distances.

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Answer:

Step-by-step explanation:

base of ladder is x feet from house

top of ladder is x+1 feet from ground

By the Pythagorean Theorem,

x² + (x+1)² = 5²

x² + (x² + 2x + 1) = 25

2x² + 2x - 24 = 0

x = -4, 3

-4 is an extraneous solution, so x = 3 ft

base of ladder is 3 feet from house

top of ladder is 4 feet from ground

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