Question

Suatu persegi panjang ABCD mempunyai panjang (3x + 2) cm, lebar (2x + 3) cm, dan luas 300 cm2. Panjang diagonal AC adalah ?

Answer 1

L = p * l
300 = (3x + 2) * (2x + 3)
300 = 6x^2 + 9x + 4x + 6
300 = 6x^2 + 13x + 6
300 - 6 = 6x^2+ 13x
294 = 6x^2 + 13x
x = 6

p = 3x + 2
p = 3(6 cm) + 2
p = 18 cm+2
p = 20 cm

l = 2x + 3
l = 2(6cm) + 3
l = 12 cm + 3
l = 15 cm

AC =
AC =
AC =
AC = 25 cm

Jadi, panjang diagonal AC adalah 25 cm.

Answer 2

L = p x l x 1/2
150 = p x l
150 = (3x + 2) x (2x + 3)
150 = 6x2 + 9x + 4x + 6
144 = 6x2 + 12x
144 = 6(x2 + 2x)
24 = x2 + 2x
x = 24/ x + 2
x = 4

diagonal^2 = (3x + 2)^2 + (2x +3)^2
diagonal = 3x +2 + 2x +3
diagonal = 5x + 5
diagonal = 5 x 4 + 5
diagonal = 25 cm