Question

Keliling persegi panjang adalah 30 cm. Tentukan panjang dan lebar agar luas maksimal!

Answer 1

A = lebar b = panjang
K = 2(2a+a)
30 = 4a + 2a
30 = 6a
a = 30/6 = 5

30 = 2(a+b)
30 = 2(5+b)
30 = 10 + 2b
20 = 2b
b = 10

Answer 2

Keliling = 2(p+l)
50 = 2(p+l)
25 = p+l ----> 25 - l = p
luas = p x l
L = (25 - l)l
L = 25l -l²

Cara 1

agar lebar maksimal maka l = 25/2
caranya 25l -l² ----> a= -1, b = 25
nilai l maksimal = -b/2a
= -25/-2
= 25/2

panjang = 50 - 25/2
panjang = 25/2

Luas maksimal = panjang x lebar
= 25/2 x 25/2
= 625/4
= 156,25

Cara 2

luas maksimal = -D/4a
D= b² - 4ac
D = (25)² -4(-1)(25)(0)
D = 625 - 0
D = 625

Luas maksimal = -625/4 x -1
= 625/4
=156,25