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2007-09-27 4:48 am
The base of a right-angled triangle is 14 cm longer than its height and 2 cm shorter than its hypotenuse
Find the length of the hypotenuse of the triangle
THZ,
吾該解釋點解會甘。

回答 (3)

2007-09-27 4:57 am
✔ 最佳答案
let x be length of the hypotenuse
base = x - 2
height = x - 2 - 14 = x - 16
(x - 2)^2 + (x - 16)^2 = x^2
x^2 - 4x + 4 + x^2 - 32x + 256 = x^2
x^2 - 36x + 260 = 0
(x - 10)(x - 26) = 0
x = 10 or x = 26
when x = 10, base = 8, height = -6 (rejected)
when x = 26, base = 24, height = 10
so length of the hypotenuse = 26

2007-09-27 5:04 am
Let x cm be the length of the hypotenuse of the triangle.

Base = x-2 cm
Height = (x-2)-14 = x-16 cm

Therefore, (x-2)^2 + (x-16)^2 = x^2
x^2 - 4x + 4 + x^2 - 32x + 256 = x^2
x^2 - 36x + 260 = 0
(x-26)(x-10) = 0
x = 26 or 10

When x = 10, height = 10-16 = -6 cm < 0, which is impossible
Therefore, x = 26, i.e. the length of hypotenuse of the triangle is 26 cm
2007-09-27 5:00 am
底比高長14cm
底比斜邊短2cm
用畢氏定理(原因係直角三角...)
條式係
設底係b,高係(b-14),斜係(b+2)
(b)2次+(b-14)2次=(b+2)2次
參考: 之後你識計啦~


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