A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out how many feet? A.) 4 feet B.) 5 feet C.) 6 feet D.) 7 feet E.) 8 feet Pythagorean Theorem a² + b² = c² {the sum of the squares of the legs equals the square of the hypotenuse} Before the ladder slips:A right triangle is formed with the hypotenuse being the ladder, itself, and the base of the building being one of the legs. a² + 7² = 25² {substituted into Pythagorean Theorem} a² + 49 = 625 {evaluated exponents} a² = 576 {subtracted 49 from both sides} a = 24 {took square root of both sides} 24 is the height of the ladder against building So, before it slips, the right triangle consists of: the ladder = 25ft {hypotenuse} the height of ladder against building = 24 ft {one leg} the distance of ladder from building = 7 ft {other leg} After it slips, the right triangle consists of: the ladder = 25 ft the height of ladder against building = 20 ft {one leg} {it slipped down 4 ft} the distance of ladder from building = unknown {other leg} a² + 20² = 25² {substituted information "after slip" into Pythagorean Theorem} a² + 400 = 625 {evaluated exponents} a² = 225 {subtracted 400 from both sides} a = 15 {took square root of both sides} After the slip, the ladder is 15 ft away from the building {and someone is probably on the ground!} Therefore, in answering the original question how many feet will the ladder slide out: It was originally 7 feet from the base and now it is 15 feet from the base, so it will slide out 8 feet. E.) 8 feet- Algebra House
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