OABC is a quadrant of a circle with center O.
OXBY is a rectangle.
If OX=4cm
YC=2cm
Find OB and the area of rectangle OXBY
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在圓形中找長方形用（畢氏定理）問題分數:10marks
2008-05-26 4:53 am
回答 (2)
2008-05-27 11:15 pm
✔ 最佳答案
Let r be the radius of the circleBy the Pythagorean theorem, we have
OX²＋OY²＝r²
＝＞ 16＋(r－2)²＝r²
＝＞ 16＋r²＋4－2．2r＝r²
＝＞ 20－4r＝0
＝＞ r＝5
Therefore,
Area of rectangle OXBY＝OX．OY＝4(r－2)＝4(5－2)＝12
2008-05-27 15:16:45 補充：
Area of rectangle OXBY＝OX．OY＝4(r－2)＝4(5－2)＝12 cm²
2008-05-30 01:25:50 補充：
OB＝r＝5 cm
2008-05-26 12:18 pm
這兒要Let 3條數式
OY + 2 = OB -------(1)
4 + AX = OB -------(2)
OY^2 + 4^2 = OB^2 -------(3) （畢氏定理）
將 (1) 代入 (3)
OY^2 + 4^2 = ( OY + 2) ^2 （畢氏定理）
OY^2 + 16 = (OY + 2) (OY + 2)
OY^2 + 16 = OY^2 + 2 OY + 2 OY + 4
16 = 4 OY + 4
4 OY = 12
OY = 3
再將 OY = 3代入式 (1)
OY + 2 = OB
3 + 2 = OB
OB = 5
OXBY 的面積是
OY x OX
= 3 x 4
=12
OY + 2 = OB
OY + 2 = OB -------(1)
4 + AX = OB -------(2)
OY^2 + 4^2 = OB^2 -------(3) （畢氏定理）
將 (1) 代入 (3)
OY^2 + 4^2 = ( OY + 2) ^2 （畢氏定理）
OY^2 + 16 = (OY + 2) (OY + 2)
OY^2 + 16 = OY^2 + 2 OY + 2 OY + 4
16 = 4 OY + 4
4 OY = 12
OY = 3
再將 OY = 3代入式 (1)
OY + 2 = OB
3 + 2 = OB
OB = 5
OXBY 的面積是
OY x OX
= 3 x 4
=12
OY + 2 = OB
收錄日期: 2021-04-15 15:04:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080525000051KK03034