Question

The lengths of diagonals of a rhombus are 24cm and 32cm. What will be the length of its altitude ?

Answer 1

given the length of diagonal of the rhombus are 24cm and 32cm respectively.

let's name them d1 and d2

first we needa find it's side and area.

let's find it's side first.

using Pythagoras theorem,

➡ h² = b² + p²

➡ side² = (d1/2)² + (d2/2)² (side is hypotenuse, and the diagonals are it's perpendicular length and base respectively u can check the attachment)

➡ side² = (12)² + (16)²

➡ side² = 144 + 256

➡ side = 400

➡ side = 20cm

the length of the side of the rhombus is 20cm.

now, there are basically two formulas to find the area of a rhombus.

one is 1/2 × d1 × d2 and the other one is base × height where base is the side of he rhombus and height is it's altitude. (since rhombus is a parallelogram too)

we are gonna use both the formulas here.

but first we've to find it's area so we'll use "1/2 × d1 × d2"

area of the rhombus = 1/2 × 24 × 32

= 12 × 32

= 384cm²

area of the rhombus is 384cm².

let's use the second formula now.

➡ base × height = 384cm²

➡ 20 × height = 384cm²

➡ height = 384/20

➡ height = 19.2cm

hence, length of it's altitude is 19.2cm