Mohon bantuannya teman2 🙂
Jawaban Terkonfirmasi
Luas segitiga = (1/2)at = (1/2).A.B
Persamaan garis, melalui (A, 0) dan (0, B)
(y – y1)/(y2 – y1) = (x – x1)/(x2 – x1)
(y – 0)/(B – 0) = (x – A)/(0 – A)
y/B = (x – A)/(-A)
-Ay = B(x – A)
B = -Ay/(x – A)
melalui (4, 3)
B = -3A/(4 – A)
(1/2).A.B = (1/2).A.(-3A/(4 – A))
= -3A²/(8 – 2A)
= 3A²/(2A – 8)
Luasnya minimum ketika turunannya = 0
Maka,
(u'v – uv')/v² = (6A(2A – 8) – 3A²(2))/(2A – 8)² = 0
6A(2A – 8) – 3A²(2) = 0
12A² – 48A – 6A² = 0
6A² – 48A = 0
6A(A – 8) = 0
A = 8
B = -3A/(4 – A)
= -3(8)/(4 – 8)
= -3(8)/(-4)
= 3(2) = 6
Maka, panjang ruasnya = √(8² + 6²) = 10