F2 畢氏定理
回答 (3)
2010-01-24 1:58 am
Let x cm be the length of height.
The length of base = 4x/3
x^2 + (4x/3)^2 = (7.5)^2 (Pyth. Theorem)
(9x^2)/9 + (16x^2)/9 = 56.25
(9x^2 + 16x^2)/9 = 56.25
25x^2 = 506.25
x^2 = 20.25
x^2 - 20.25 = 0
x^2 - (4.5)^2 = 0
(x + 4.5) (x - 4.5) = 0
x + 4.5 = 0 OR x - 4.5 = 0
The length of base = 4x/3
x^2 + (4x/3)^2 = (7.5)^2 (Pyth. Theorem)
(9x^2)/9 + (16x^2)/9 = 56.25
(9x^2 + 16x^2)/9 = 56.25
25x^2 = 506.25
x^2 = 20.25
x^2 - 20.25 = 0
x^2 - (4.5)^2 = 0
(x + 4.5) (x - 4.5) = 0
x + 4.5 = 0 OR x - 4.5 = 0
2010-01-19 3:05 am
斜邊7.5cm,底邊是高的三分之四,求高幾cm ?
設該三角形的高是x cm。
在該直角三角形中，
(4x/3)^2+x^2=7.5^2(畢氏定理)
(16x^2/9)+x^2=56.25
9（16x^2/9+x^2)=9(56.25)
16x^2+9x^2=506.25
25x^2=506.25
x^2=20.25
x=√20.25
x=4.5 and -4.5
∵三角形的边長不可能是負数。
∴該三角形的高是4.5cm。
設該三角形的高是x cm。
在該直角三角形中，
(4x/3)^2+x^2=7.5^2(畢氏定理)
(16x^2/9)+x^2=56.25
9（16x^2/9+x^2)=9(56.25)
16x^2+9x^2=506.25
25x^2=506.25
x^2=20.25
x=√20.25
x=4.5 and -4.5
∵三角形的边長不可能是負数。
∴該三角形的高是4.5cm。
參考: need not to know
2010-01-19 2:23 am
Let the heeeight be x cm, i.e. the base is 4x/3 cm,, suppose height perpendicular to base,
By Pyth. Theorem,
(x)^2+(4x/3)^2=7.5^2
x^2+ (16x^2)/9 = 56.25
9x^2 + 16x^2 = 506.25
25x^2 - 506.25 = 0
x^2 - 20.25 = 0
(x-4.5)(x+4.5)=0
x=4.5 or -4.5(rej, x>0)
Hence, the height is 4.5 cm
By Pyth. Theorem,
(x)^2+(4x/3)^2=7.5^2
x^2+ (16x^2)/9 = 56.25
9x^2 + 16x^2 = 506.25
25x^2 - 506.25 = 0
x^2 - 20.25 = 0
(x-4.5)(x+4.5)=0
x=4.5 or -4.5(rej, x>0)
Hence, the height is 4.5 cm
參考: Hope can help you~~
收錄日期: 2021-04-13 17:03:01
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