Question

The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is ______.

विकल्प

• 12cm

• 12.8cm

• 19cm

• 19.2cm

Answer 1

The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is 19.2cm.

Explanation:-

Area of the Rhombus ${\displaystyle =\frac{1}{2}{d}_1{d}_2=\frac{1}{2}\times 24\times 32=384{\text{cm}}^2}$

Using Pythagoras theorem

${\displaystyle {\text{side}}^2={\left(\frac{1}{2}{d}_1\right)}^2+{\left(\frac{1}{2}{d}_2\right)}^2={12}^2+{16}^2=144+256=400}$

Side = 20cm

Area of the Rhombus = base × altitude

384 = 20 × altitude

So altitude = ${\displaystyle \frac{384}{20}}$ = 19.2cm