Area of a rhombus is 108 cm². If the sum of the length of its diagonals is 30…
2021
Area of a rhombus is 108 cm². If the sum of the length of its diagonals is 30 cm, then what will be the difference between the length of its diagonals?
- A.
8 cm
- B.
6 cm
- C.
4 cm
- D.
12 cm
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Area of rhombus = (1/2) * d1 * d2 = 108 cm².
Product of diagonals (d1 * d2) = 108 * 2 = 216 cm².
We are given the sum of diagonals (d1 + d2) = 30 cm.
Apply the algebraic identity: (d1 + d2)² - (d1 - d2)² = 4 * d1 * d2.
Substitute the values: (30)² - (d1 - d2)² = 4 * 216.900 - (d1 - d2)² = 864.
(d1 - d2)² = 900 - 864 = 36.
Difference (d1 - d2) = sqrt(36) = 6 cm.
Final Answer: Option 2