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小 發表於 2020-11-3 06:28 PM (第 1242 天)
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known:
1. DE = FG = k
2. AC = 5 (pyth thm)
3. shortest distance from B to AC
thus height of triangle BDG = (a) - k
let DG = EF = y, Area of DEFG = ky
let AE = x, then FC = 5-x-y
AND, Area DEFG = Area of triangle ABC - (Area of triangle BDG + Area of triangle ADE + Area of triangle FCG)
= 3x4/2 - {y[(a)-k]/2 + kx/2 + k(5-x-y)/2}
= 6 - {y[(a)-k]/2 + kx/2 + (5k-kx-ky)/2}
= 6 - {y[(a)-k]/2 + kx/2 + 5k/2 - kx/2 - ky/2}
= 6 - {y[(a)-k]/2 + 5k/2 - ky/2}
Solve for y
如果佢等於5/12(12-5k)可以嗎?
p.s. Area of DEFG = ky = k [5/12(12-5k)]