find the area of the rhombus whose side is 5cm and whose altitude is 4.8cm if one of its diagonal is 8cm long find the length of the other diagonal
Answers
Area of the rhombus = Side × Length of the altitude
= 5*4.8
= 24 sq cm
Now,
Let the length of the other diagonal = x
It is known that the area of a rhombus is half the product of its diagonals.
∴ (1/2) × 8 × x = 24
⇒ 4x = 24
⇒ x = 6 cm
The length of the other diagonal is 6 cm.
hope it'll help :)
Answer:
Given:-
The area of rhombus, side is 5cm and altitude is 4.8cm and one of its diagonal is 8cms.
To Find:-
Find the length of other diagonal. ....?
Solutions:-
Let the length of the other diagonal of the rhombus be x.
A rhombus is a special are of a parallelogram.
The area of a parallelogram is the product of its base and height.
Area of the Rhombus = base × height
= 5cm × 4.8cm
= 24cm²
Area of rhombus = 1/2 (products of its diagonal)
⟹ 24cm² = 1/2 × (8cm + x)
⟹ x = 24 × 2 / 8
⟹ x = 48/8
⟹ x = 6cm
Hence, the length of the other diagonal of the Rhombus is 6cm.
Some Important:-
A rhombus all side are equal.
A rhombus opposite angle are equal.
A rhombus the sum of adjacent angle angle supplementary i.e. (<A + <D = 180°).
A rhombus, each diagonal of a rhombus divides it into two congruent triangle.
A rhombus, if one angle is right, then all angle are right.
Diagonal of a rhombus bisect each other and also perpendicular to each other.
More important:-
Area of rhombus = b × h
Perimeter of rhombus = 4 × side
where,
b = base
h = height
p = perimeter
a = area