If the area of a rhombus is 720 cm2 and the length of one of the two diagonals is 80 cm then find the length of each side of the rhombus.
1. 82 cm
2. 41 cm
3. 18 cm
4. 40 cm
If the area of a rhombus is 720 cm2 and the length of one of the two diagonals is 80 cm then find the length of each side of the rhombus.
1. 82 cm
2. 41 cm
3. 18 cm
4. 40 cm
1. 82 cm
2. 41 cm
3. 18 cm
4. 40 cm
Correct Answer – Option 2 : 41 cm
Given:
Area of a rhombus = 720 cm2
Length of first diagonal = 80 cm
Concept used:
The two diagonals bisect each other at 90° in a rhombus.
Formula used:
Area of rhombus = (1/2) × Product of the two diagonals
Calculations:
Let the length of second diagonal be x
Area of rhombus = (1/2) × 80 × x
⇒ 720 = (1/2) × 80x
⇒ x = 18 cm
If the two diagonals of rhombus ABCD intersect at O then,
⇒ AO2 + BO2 = AB2
⇒ (80/2)2 + (18/2)2 = AB2
⇒ AB2 = 402 + 92
⇒ AB2 = 1600 + 81
⇒ AB2 = 1681
⇒ AB = 41 cm
∴ The length of each side of a rhombus is 41 cm.