The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the
altitude of the rhombus is
(a) 12cm (b) 12.8cm (c) 19 cm (d) 19.2cm
Answers
The diagonals of a rhombus bisect each-other at right angles,with the side of the rhombus being the hypotenuse . Half the lengths of the diagonals AO = 12 cm , BO= 16 cm. and the hypotenuse(AB) in right triangle ABO in rhombus ABCD.
Using Pyhagoras Theorem for the right-angled triangle ABO,
h² = 12² + 16² = 400.
∴ The length of the side of the rhombus is 20 cm.
area of a rhombus = ½×d1×d2
are of a rhombus= base × height
∴ comparing both formulas
½×24×32 = 20×h (base is side of the rhombus)
∴ h= 19.2 cm.
Given : The lengths of the diagonals of a rhombus are 24cm and 32cm,
To Find : the length of the altitude of the rhombus
Solution:
lengths of the diagonals of a rhombus are 24cm and 32cm,
Area = (1/2) * 24 * 32 = 12 * 32
= 384 cm²
Diagonals bisect each other perpendicularly
Hence Half of diagonal = 12 cm and 16 cm
and Side of rhombus = √12² + 16²
= 20 cm
Area = base * altitude
= 20 * altitude
20 * altitude = 384
=> altitude = 19.2 cm
Learn More:
If the area of a trapezium with parallel sides of length 30 cm and 23 ...
brainly.in/question/4717262
Find the area of trapezium in which parallel sides are of length 5 cm ...
brainly.in/question/3877026