數 - ( 26 ) 等腰三角形

One 等腰三角形 have one short line and two long line , the short one is the
long one ' s 1 / 2 , 周界 = 40 cm , 求 area .

首先設等腰三角形的腰是a，最短的叫b
周界=40
a+a+b=40
2a+b=40----(1)

b=a/2---(2)

(2)代入(1)
2a+a/2=40
4a+a=80
5a=80
a=16

把a=16代入(2)
b=16/2=8

所以等腰三角形邊長是16cm, 16cm, 8cm

因為是等腰三角形，等腰三角形的高線會平分底
設三角形的高為h
h^2+(8/2)^2=16^2(畢氏定理)
h^2+4^2=16^2
h^2=256-16
h^2=240=16x15
h=4sqrt15

面積
=8x4sqrt15/2
=16sqrt15(cm^2)

2010-06-30 12:01:23 補充：
我自己諗ga.....=.=

2010-06-30 12:46:45 補充：
Vic計面積的方法是用了希羅公式(heron's formula)
此公式是用來計三角形面積
已知三條邊的長度所求的area
方法是
先求半周界s=(a+b+c)/2, a, b, c是長度
然後用此公式求面積
A^2=s(s-a)(s-b)(s-c)

Sorry,I am very careless!!

2010-06-30 12:00:37 補充：
Let x to a long side:
x+x+(x/2)=40
2.5x =40
x =16

Length of a short side:
16/2
=8

Half of a short side:
8/2
=4
Let h to the height of triangle:
4^2+h^2=16^2
h^2 =240
h =4sqrt15
The are of triangle:
8(4sqrt15)/2
16sqrt15cm^2

Let x be the length of the longer line.
The length of the short line will be x/2.

The perimeter :
x+x+x/2=40
x=16
Length of the short line = 16/2=8

Let h be the height of the triangle, by P's theorem

h^2 + 4^2 = 16^2
h^2 = 240
h = 15.49

area = 8 x 15.49 /2 =61.96cm^2

圖片參考：http://a.imagehost.org/0979/ScreenHunter_02_Jun_29_15_35.gif


http://a.imagehost.org/0979/ScreenHunter_02_Jun_29_15_35.gif