Question : 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
Doubt by Vanshika & Pushkar
Solution:
d1=24 cm
d2 = 32 cm
a=side of the Rhombus (Let)
We know, diagonals of rhombus bisect each other at 90°
By Pythagoras Theorem
a2=(d1/2)2+(d2/2)2
a2= (24/2)2+(32/2)2
a2 = (12)2+(16)2
a2 = 144 + 256
a2 = 400
a = √(400)
a = 20 cm
a2=(d1/2)2+(d2/2)2
a2= (24/2)2+(32/2)2
a2 = (12)2+(16)2
a2 = 144 + 256
a2 = 400
a = √(400)
a = 20 cm
Area of Rhombus = ½×(Product of its diagonals)
=½(d1×d2)
=½×24×32 --------(1)
=½(d1×d2)
=½×24×32 --------(1)
Also,
Rhombus is also a parallelogram.
Area of Rhombus
= Base × Perpendicular Height
½×24×32 = a × H [Using eq (1)]
½×24×32 = 20×H
12×32 = 20×H
(12×32)/20 = H
(12×16)/10 = H
192/10 = H
19.2 =H
H = 19.2 cm
∴ Length of the altitude of Rhombus is 19.2 cm
Rhombus is also a parallelogram.
Area of Rhombus
= Base × Perpendicular Height
½×24×32 = a × H [Using eq (1)]
½×24×32 = 20×H
12×32 = 20×H
(12×32)/20 = H
(12×16)/10 = H
192/10 = H
19.2 =H
H = 19.2 cm
∴ Length of the altitude of Rhombus is 19.2 cm
Hence, d) is the correct option.