OG详解-OG6 数学2 Q22

Choice B is correct. The Pythagorean theorem states that for a right triangle, c² = a² +b², where c represents the length of the hypotenuse and a and b represent the lengths of the legs. It’s given that in triangle ABC, angle B is a right angle. Therefore, triangle ABC is a right triangle, where the hypotenuse is side AC and the legs are sides AB and BC. It’s given that the lengths of sides AB and BC are 10 √37​ and 24√37​ , respectively. Substituting these values for a and  b in the formula c² = a² +b²  yields c² = (10 37)² +(24 37)² , which is equivalentChoice B is correct. The Pythagorean theorem states that for a right triangle, c² = a² +b², where c represents the length of the hypotenuse and a and b represent the lengths of the legs. It’s given that in triangle ABC, angle B is a right angle. Therefore, triangle ABC is a right triangle, where the hypotenuse is side AC and the legs are sides AB and BC. It’s given that the lengths of sides AB and BC are 10 √37​ and 24√37​, respectively. Substituting these values for a and  b in the formula c² = a² +b²  yields c² = (10 37)² +(24 37)² , which is equivalent to c² = 100(37)+576(37), or c² = 676(37). Taking the square root of both sides of this equation yields c = ±26 37 . Since c represents the length of the hypotenuse, side AC, c must be positive. Therefore, the length of side AC is 26 √37​.
Choice A is incorrect. This is the result of solving the equation c = 24√37​- 10√37​, not c² = (10√37​ )² +(24√37​)² . Choice C is incorrect. This is the result of solving the equation c = 10 √37​ +24√37​, not c² = (10√37​ )² +(24√37​ )² . Choice D is incorrect and may result from conceptual or calculation errors.