Penjelasan dengan langkah-langkah:
Misalkan :
x = panjang
y = lebar
K = keliling persegi panjang
L = Luas persegi panjang
K = 2x + 2y
2x + 2y = 200
x + y = 100
y = 100 - x
L = x . y
L = x (100 - x)
L(x) = - x² + 100x
L' (x) = - 2x + 100
L' (x) = 0
- 2x + 100 = 0
2x = 100
x = 100/2 = 50
L (50) = - (50²) + 100 (50)
L (50) = - 2500 + 5000
L (50) = 2500
Luas maksimum adalah 2500 cm².
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Verified answer
Penjelasan dengan langkah-langkah:
Misalkan :
x = panjang
y = lebar
K = keliling persegi panjang
L = Luas persegi panjang
K = 2x + 2y
2x + 2y = 200
x + y = 100
y = 100 - x
L = x . y
L = x (100 - x)
L(x) = - x² + 100x
L' (x) = - 2x + 100
L' (x) = 0
- 2x + 100 = 0
2x = 100
x = 100/2 = 50
L (50) = - (50²) + 100 (50)
L (50) = - 2500 + 5000
L (50) = 2500
Luas maksimum adalah 2500 cm².