Explanation:
the area of a rectangle is
length × width
the perimeter of a rectangle is
2×length + 2×width
so,
length×width = 48 cm²
2×length + 2×width = 28 cm
length + width = 14 cm
length = 14 - width
we use this in the first equation :
(14 - width) × width = 48
14×width - width² = 48
-width² + 14×width - 48 = 0
a quadratic equation
ax² + bx + c = 0
has the general solution
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = -1
b = 14
c = -48
width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =
= (-14 ± sqrt(196 - 192))/-2 =
= (-14 ± sqrt(4))/-2 =
= (-14 ± 2)/-2 =
= 7 ± 1
width1 = 7 + 1 = 8 cm
width2 = 7 - 1 = 6 cm
length1 = 14 - width1 = 14 - 8 = 6 cm
length2 = 14 - width2 = 14 - 6 = 8 cm
so, we see, one of them must be 8 cm, and the other 6 cm.
let's length be the longer side, so
length = 8 cm
width = 6 cm