Pythagoras' Theorem (畢氏定理) 10點

2012-04-22 7:31 pm

As shown in the figure , a piece of wire ( the solid line ) is bent into an L-shape . The shape can be formed by two squares of areas 25平方厘米 and 9平方厘米.
(a) What is the length of the wire?
(b) If the wire is bent again into a square , what is the change in the area enclosed when compared with original L-shape?



圖片參考:http://imgcld.yimg.com/8/n/HA06650353/o/701204220023913873397480.jpg


In the figure , 角B=90度 , E is a point on AC such that AE = AB and AE : AC = 1 : 2 . If BC = 32 cm , find AC.

圖片參考:http://imgcld.yimg.com/8/n/HA06650353/o/701204220023913873397481.jpg
更新1:

To:Tsz Wing 第2題個答案好似係33.9cm ( 由於本人唔係幾知條式點計,但係本書有個正確答案,所以我想請問第2題嘅算式係咪有少少錯左?希望你能再次幫我解答,Thanks)

回答 (2)

2012-04-22 11:15 pm
✔ 最佳答案
1a) 因為ABCD是正方形且面積是25平方厘米,所以AB=BC=CD=DA=5cm,同樣地,GF=FE=ED=DG=3cm
所以,the length of the wire
= AB+BC+CD+DE+EF+FG+(AD-GD)
=26cm
b)因為the length of the wire 是26cm,所以每條邊長是6.5cm
新正方形面積
=6.5x6.5=42.25平方厘米
相比原先圖形的面積(34平方厘米)多了8.25平方厘米
2)let AB =x cm

因為AE:AC=1:2

所以AE=EC=AB= x cm

(2x)^2 -(32)^2 + x^2 (畢氏定理)

x=18.48cm
所以AC=2x=36.95cm




2012-04-22 15:16:01 補充:
若有任何錯誤請提出
參考: 自己
2012-04-23 6:19 pm
條題目如果係 AE : EC = 1 : 2,就係 33.94cm
條題目如果係 AE : AC = 1 : 2,就係 36.95cm


收錄日期: 2021-04-28 14:20:57
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120422000051KK00239

檢視 Wayback Machine 備份