Question

The diagonals of a rhombus are in the ratio $3:4$. If its perimeter is $40cm$, find the length of the sides and diagonals of the rhombus.

Answer 1

R.E.F image

Let the sides of rhombus be a

and diagonals be $d_1$ and $d_2$

perimeter $=40cm$

$4a=40cm$

$a=10cm$

Ratio of diagonals$=3:4$

$\frac{d_1}{d_2}=\frac{3}{4}$

$d_1=\frac{3d_2}{4}$ ...(1)

Now,

$a^2=\frac{d_1^2}{4}+\frac{d_2^2}{4}$

$d_1^2+d_2^2=4a^2$

$\frac{9d_2^2}{16}+d_2^2=4(10{)}^2$

$\frac{25d_2^2}{16}=400$

Square Rooting both sides

$\frac{5d_2}{4}=20$

$d_2=16$

put $d_2=16$ in equation ...(1)

$d_1=12$