Question

The length of the diagonals of a rhombus are in the ratio 3:4. If its area is $216c{m}^2$, then its side is ___ cm.

• A. 25
• B. 35
• C. 36
• D. 30

Answer 1

The correct option is C

36

Let the diagonals be $3\times$ and $4\times$ Area of rhombus $=\frac{1}{2}\times$ Product of diagonals

$216=\frac{1}{2}(3\times )(4\times )$

$216=6x^2$

$36=x^2$

$\therefore x=6cm$

$\therefore$ The diagonals are 18 cm and 24 cm we know that diagonals of a rhombus bisect each other at right angles.

$\therefore$ Suppose A0 = 9 cm and B0 = 12 cm

then $A{B}^2=9^2+{12}^2$ (9-12-15 pythagoras Triplet)

$={15}^2$ $\therefore AB=15cm$

Hence (c)