數學知識交流---Poly U Math 20120101
2011-11-02 5:40 am
A line L:3x+4y-k=0 which k>0 cut the x-axis and y-axis at A&B repectively,if area of tri. AOB=24sq units,find k
回答 (1)
2011-11-02 6:12 am
✔ 最佳答案
Let A = (a,0) and B = (0,b)Put x = a and y = 0,
3a - k = 0
3a = k ---(1)
Put x = 0 and y = b,
4b - k = 0
4b = k ---(2)
3a = 4b
Hence a:b = 4/3
Let a = 4h and b = 3h
Since the area of triangle AOB = 24 sq. units
(1/2)(4h)(3h) = 24
12h^2 = 48
h^2 = 4
h = 2 or -2
For h = 2, a = 8 and b = 6,
therefore k = 24
For h = -2, a = -8 and b = -6,
therefore k = -24 (rejected) for k > 0
參考: Knowledge is power.
收錄日期: 2021-04-23 20:48:04
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111101000051KK00937