Question

Find the area of a rhombus whose side is $5cm$ and whose altitude is $4.8cm$. If one of its diagonal is $8cm$ long, find the length of the other diagonal.

Answer 1

Given:

Side of the rhombus $=5cm$

Altitude of the rhombus $=4.8cm$

We know that, Rhombus is a parallelogram.

Area of Parallelogram $=$ Base $\times$ Corresponding height

$\Rightarrow$ Area of the rhombus $=$ Side $\times$ Length of the altitude
$=5cm\times 4.8cm$
$=24c{m}^2$

Therefore, Area of the rhombus $=$ $24c{m}^2$
Now, in rhombus

it is given that, one of the diagonal $\left(d_1\right)=8cm$
Let the length of the other diagonal $\left(d_2\right)=x$
Area of rhombus $=\frac{1}{2}\times d_1\times d_2$
$\Rightarrow 24c{m}^2=\frac{1}{2}\times 8cm\times x$
$\Rightarrow 24cm=4x$

$\Rightarrow \frac{24cm}{4}=x$

$\Rightarrow 6cm=x$
Therefore, the length of the other diagonal is $6cm$.