9. The length of one diagonal of a rhombus
is less than the second diagonal by 4 cm. The area of the rhombus is 30 sq.cm.
Find the length of the diagonals.
Sol. Let the
length of second diagonal of a rhombus be ‘x’ cm.
∴ the length of
first diagonal of a rhombus = x – 4
Area of rhombus =
½ × Product of length of diagonals
Area of rhombus =
½ (x) (x – 4)
According to
given condition,
½
(x) (x – 4) = 30
∴ x ( x – 4) = 60
∴ x2 –
4x = 60
∴ x2 –
4x – 60 = 0
∴ x2 –
10x + 6x – 60 = 0
∴ x(x – 10) + 6(x
– 10) = 0
∴ (x – 10) (x + 6
) = 0
∴ x – 10 = 0 or x + 6 = 0
∴ x = 10 or x = - 6
∵ The length of
diagonal of the rhombus cannot be negative.
∴ x = 10
∴ x – 4 = 10 – 4 =
6
∴ The length of first
diagonal of a rhombus is 6 cm and second diagonal is 10 cm.
