Question

The area of a rhombus is equal to the area of a triangle having base $24.8cm$ and corresponding height $16.5cm$. If one of the diagonals of the rhombus is $22cm$, find the length of the other diagonal.

Answer 1

For Triangle:

Base $=24.8cm$

Height $=16.5cm$

Area of triangle $=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 24.8\times 16.5$

$=204.6c{m}^2$

For Rhombus:

One diagonal of rhombus $d_1=22cm$

Let other diagonal be $d_2$.

Area of rhombus $=\frac{d_1{d}_2}{2}$

$=\frac{22\times d_2}{2}$

$=11d_{2}c{m}^2$

Now,

It is given that,

Area of rhombus $=$ Area of triangle

$\therefore$ $11d_2=204.6$

$\Rightarrow$ $d_2=\frac{204.6}{11}$

$\therefore$ $d_2=18.6cm$