3. The length of the rectangle is greater
than its breadth by 2 cm. The area of the rectangle is 24 sq.cm, find its
length and breadth.
Sol. Let the breadth of the rectangle be
‘x’ cm.
∴ It’s
length is (x + 2) cm.
As per the given condition.
∴ Area
of rectangle = Length × Breadth
∴ 24
= (x + 2) x
∴ 24
= x2 + 2x
∴ 0
= x2 + 2x – 24
∴ x2
+ 2x – 24 = 0
∴ x2
– 4x + 6x – 24 = 0
∴ x
(x – 4) + 6(x – 4) = 0
∴ (x
– 4) (x + 6) = 0
∴ x
– 4 = 0 or x + 6 = 0
∴ x
= 4 or x = -6
∴ The
breadth of rectangle cannot be negative.
∴ x cannot
be negative
∴ x
= 4 and
x +
2 = 4 + 2 = 6
∴ The
length of rectangle is 6 cm and its breadth is 4 cm.
