# The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively.

Question:

The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively. If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.

Solution:

Given:

Area of the rhombus = Area of the triangle with base $24.8 \mathrm{~cm}$ and altitude $16.5 \mathrm{~cm}$

Area of the triangle $=\frac{1}{2} \times$ base $\times$ altitude $=\frac{1}{2} \times 24.8 \times 16.5=204.6 \mathrm{~cm}^{2}$

$\therefore$ Area of the rhombus $=204.6 \mathrm{~cm}^{2}$

Also, length of one of the diagonals of the rhombus $=22 \mathrm{~cm}$

We know : Area of rhombus $=\frac{1}{2}\left(d_{1} \times d_{2}\right)$

$204.6=\frac{1}{2}\left(22 \times d_{2}\right)$

$22 \times d_{2}=409.2$

$d_{2}=\frac{409.2}{22}=18.6 \mathrm{~cm}$

Hence, the length of the other diagonal of the rhombus is $18.6 \mathrm{~cm}$.