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【OG20-P292-442题】
The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?
(1) The area of the triangle is 25 square centimeters.
(2) The 2 legs of the triangle are of equal length.
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分析A选项
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分析B选项
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分析C选项
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分析D选项
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分析E选项
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题干：设两直角边是a,b，斜边是c。c=10,a^2+b^2=100
条件1：ab=50→(a-b)^2=0→a=b=5√2，充分
条件2：a=b=5√2，充分
题目讨论 （4条评论）
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贾思敏
做条件一的时候有点卡壳，其实就是给出了a^2+b^2=100, ab=50即2ab=100，所以（a-b）^2=0，也就是说a=b，就是ab=a^2=b^2=50，所以a=b=5倍根号下2，那么C=a+b+c的值就可以求出来了 条件二：a=b的话，就是2a^2=100，a=b=5倍根号下2，同理，周长可以求出来。
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2021-10-04 19:27:53
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kikig
x^2+y^2= 100 (Pyth Theorem).....1) 2xy=100.........................2) Adding 1) and 2) (x+y)^2= 200 or x+y=10 sqroot 2 (Hence statement 1 is sufficient) or Perimeter = x+y+10 = 10(1+sq.rt2) Statement 2. 2x^2=100; x=5 sqrt2 Perimeter = 10 (1+sqrt2)..(Hence, statement 2 is sufficient) As both statements are sufficient. Hence, D
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2019-12-21 09:01:51
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cbc021
可以从毕达哥拉斯定理（勾股定理）的英文版熟悉直角三角形相关的英文词汇： Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse. 条件1： 不妨假设直角边分别为x、y，则由题意和条件可得： x^2+y^2=100 xy=50 欲求x+y+10=? 即求x+y=? 而x+y=sqr((x+y)^2)=sqr(x^2+y^2+2xy)=sqr(200) 故可以得到唯一确定的三角形周长，充分 条件2显然 故选D
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2018-02-21 13:16:59
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Jaris+
注意是直角三角形
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2017-11-26 11:22:46
