Question

There is a rhombus of side 6 cm and altitude 4 cm. If one of the diagonals is 8 cm long, find the length of the other diagonal

Answer 1

Since rhombus is also a kind of Parallelogram.
$\therefore$ Area of rhombus = Base $\times$ Altitude
= $6\times 4=24c{m}^2$ [1 mark]
Also, Area of rhombus = $\frac{1}{2}{d}_1{d}_2$
$\Rightarrow 24=\frac{1}{2}\times 8\times d_2\Rightarrow 24=4d_2$ [1 mark]
$\Rightarrow d_2=\frac{24}{4}=6cm$ [1 mark]
Hence the length of the other diagonal is 6 cm.