In triangle ABC, angle B is a right angle. The length of side AB is 10√37 and the length of side BC is 24√37. What is the length of the side AC?
Correct answer: B. 26√37
- A. 14√37
- B. 26√37
- C. 34√37
- D. √(34.37)
Explanation
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 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.
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