Question

The area of a rhombus is equal to the area of a triangle. If base of A is 24 cm, its corresponding altitude is 16 cm and one of the diagonals of the rhombus is 19.2 cm. Find its other diagonal.

Answer 1

Area of a rhombus =Area of a triangle

Base of triangle =24 cm

and altitude =16 cm

$\therefore$ Area $=\frac{1}{2}$ base $\times$ altitude

$=\frac{1}{2}\times 24\times 16=192c{m}^2$

$\therefore$ Area of rhombus =192 $c{m}^2$

One diagonal =19.2 cm

$\therefore$ Second diagonal $=\frac{Area\times 2}{\text{One diagonal}}$

$=\frac{192\times 2}{19.2}=\frac{192\times 10\times 2}{192}=20cm$