find the length of a altitude of a rhombus if lengths of its diagonals are 12cm and16cm respectively.
Answers
Answer: 9.6 cm
Step-by-step explanation:
Given,
Length of one diagonal = 12cm
Length of other diagonal = 16cm
The diagonal of rhombus bisect each other at right angle.
Now,
Take one of the part out of four part formed by the two diagonal to find out the side of the Rhombus
One of the side is 6 cm= half of the one diagonal(12 cm)
Other side is 8 cm, half of the other diagonal (16cm)
By using Pythagoras theorem,
(Side of rhombus)^2 = 6^2+8^2
On solving,
You get
Side of the Rhombus = 10 cm
Adjacent side of the Rhombus are equal.
Rhombus is also known as parallelogram.
Now,
Area of the parallelogram= Area of rhombus
Area of rhombus =1/2*( product of the length if the diagonal)
Area of the parallelogram = base*height
Base = 10 cm
Now,
10* height = 1/2 *(12*16)
10* height = 96
Height = altitude = 96/10
9.6 cm