Question

The area of the rhombus is 48 $c{m}^2$, If the diagonals of rhombus are in ratio 3:2, then find the length of each diagonal.

• A. 8 cm, 6 cm
• B. 9 cm, 6 cm
• C. 10 cm, 8 cm
• D. 12 cm, 8 cm

Answer 1

The correct option is D 12 cm, 8 cm

Let the length of the diagonals be 3y and 2y.
Area of rhombus = $\frac{1}{2}$$\times$(Product of diagonals)
Area of rhombus = $\frac{1}{2}$$\times$(3y$\times$2y)
48 = 3$y^2$
$y^2$ = $\frac{48}{3}$ = 16
y = $\sqrt{1}6$ = 4
Hence, the length of diagonals are 3y, 2y i.e 12 cm, 8 cm.