Question

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

Options

• 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 `=1/2 d_1d_2=1/2xx24xx32=384 "cm"^2`

Using Pythagoras theorem

`"side"^2=(1/2d_1)^2+(1/2d_2)^2=12^2+16^2=144+256=400`

Side = 20cm

Area of the Rhombus = base × altitude

384 = 20 × altitude

So altitude = `384/20` = 19.2cm