Question

Find the area of a rhombus whose side is $6cm$ and whose altitude is $4cm.$ If one of its diagonals is $8cm$ long, find the length of the other diagonal.

Answer 1

Given: Side of rhombus, $\left(b\right)=6cm$

Altitude $\left(h\right)=4cm$

And, the length of one diagonal, $d_1=8cm$

We know that the rhombus is a parallelogram.

Area of given rhombus $ABCD=$ base $\times$ height [$\because$ Area of parallelogram $=$ base $\times$ height ]

$=b\times h=6\times 4c{m}^2=24c{m}^2$

Also, Area of rhombus is given by formula: Area $=\frac{1}{2}\times d_1\times d_2$

So, Area of given rhombus ABCD $=\frac{1}{2}\times 8\times d_2$

$\therefore 24=\frac{1}{2}\times 8\times d_2$

$\Rightarrow d_2=\frac{24\times 2}{8}=6cm$

Hence, the length of the other diagonal is $6cm.$