Question

Q.4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is a) 12 cm b) 12.8 cm c) 19 cm d) 19.2 cm​

Answer 1

Answer:

d) 19.2 cm

Step-by-step explanation:

the lengths of the diagonals of a rhombus are 24 cm and 32 cm.

then the half measurements of the lengths are 12cm and 16cm.

if the measurement of each side of the rhombus is l ,

then, l^2 = 12^2 + 16^2 = 144 + 256 = 400

i.e., l = 400^(1/2) = 20

now area of the rhombus is

1/2 × diagonal 1 × diagonal 2

= 1/2 × 24 × 32 = 384 cm^2

now area of a rhombus

= side of the rhombus × altitude of the rhombus

so, the altitude of the rhombus

= area of the rhombus / side of the rhombus

= 384 / 20 = 19.2 cm