2. 外语
  3. In right triangle ABC, the ratio of the lengths of the two legs is 2 to 5. If the area of triangle ABC is 20, what is the length

In right triangle ABC, the ratio of the lengths of the two legs is 2 to 5. If the area of triangle ABC is 20, what is the length

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问题 In right triangle ABC, the ratio of the lengths of the two legs is 2 to 5. If the area of triangle ABC is 20, what is the length of the hypotenuse?
选项 A、7
B、10
C、
D、
E、
答案E
解析 The ratio of the lengths of the legs of right triangle ABC is 2 to 5, so you can represent the lengths as 2x and 5x, respectively, where x>0. Since the area of the triangle is 20, it follows that= 20. Solving this equation for x gives x = 2. So the lengths of the two legs are 2(2)and 2(5), or 4 and 10, respectively. Therefore, by the Pythagorean theorem, the length of the hypotenuse is. This square root can be simplified as follows.

The correct answer is Choice E.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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