#### 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 cm and altitude 16.5 cm

\[\text{ Area of the triangle }=\frac{1}{2}\times\text{ base }\times\text{ altitude }=\frac{1}{2} \times24.8\times16.5=204.6 cm^2 \]

∴ Area of the rhombus = 204.6 cm^{2}

Also, length of one of the diagonals of the rhombus=22 cm

We know: Area of rhombus \[=\frac{1}{2}( d_1 \times d_2 )\]

\[204 . 6 = \frac{1}{2}(22 \times d_2 )\]

\[22 \times d_2 =409.2\]

\[ d_2 =\frac{409 . 2}{22}=18.6 cm\]

Hence, the length of the other diagonal of the rhombus is 18.6 cm.