Question

Diagonals of a rhombus are in ratio 4:3. find their lengths if area of that rhombus is 24$c{m}^2$.

• A. 3 cm, 4 cm
• B. 6 cm, 8 cm
• C. 9 cm, 12 cm
• D. 12 cm, 16 cm

Answer 1

The correct option is B 6 cm, 8 cm

Let common multiple of length of the diagonals be y.

According to given condition
Area of rhombus = $\frac{1}{2}$$\times$(product of diagonals)
24 = $\frac{1}{2}$$\times$(4y$\times$3y) = 6y
$y^2$ = $\frac{24}{6}$ = 4
y = $\sqrt{4}$
$⟹$y = 2
Hence
Lengths of diagonals are 3y and 4y.
diagonal 1 = 3y = 3$\times$2 = 6 cm.
diagonal 2 = 4y = 4$\times$2 = 8 cm.