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Area of rhombus is (7 + 6.5√5) cm2 and length of its one diagonal is (3 + 2√5) cm, then what is the length of its second diagonal?
  • a)
    (8 + √5) cm
  • b)
    (6 - 2√5) cm
  • c)
    (8 + 3√5) cm
  • d)
    (8 - √5) cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Area of rhombus is (7 + 6.5√5) cm2 and length of its one diagonal is ...
Area of rhombus = (First diagonal x Second diagonal) / 2
2 x Area of rhombus = (First diagonal x Second diagonal)
Let its second diagonal = (a + b√5) cm
(14 + 13√5) = (3 + 2√5) x (a + b√5)
(14 + 13√5) = (3a + 3b√5 + 2a√5 + 10b)
After comparing-
(3a + 10b) = 14 ...... (1)
(2a + 3b) = 13 ....... (2)
From (1) and (2)-
a = 8 and b = -1
Length of second diagonal = (a + b√5) = (8 - √5) cm
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Most Upvoted Answer
Area of rhombus is (7 + 6.5√5) cm2 and length of its one diagonal is ...
Given information:
- Area of rhombus: (7 + 6.5√5) cm²
- Length of one diagonal: (3 + 2√5) cm

Finding the length of the second diagonal:

1. Area of a rhombus:
The area of a rhombus can be calculated using the formula:
Area = (1/2) * d1 * d2, where d1 and d2 are the diagonals of the rhombus.
Given that the area of the rhombus is (7 + 6.5√5) cm², we have:
(7 + 6.5√5) = (1/2) * (3 + 2√5) * d2

2. Solving for the length of the second diagonal:
Multiplying both sides by 2 to eliminate the fraction, we get:
14 + 13√5 = (3 + 2√5) * d2
Expanding the right side of the equation:
14 + 13√5 = 3d2 + 2√5d2
Now, comparing the coefficients of √5 on both sides, we get:
13 = 2d2
d2 = 13/2 = 6.5
Therefore, the length of the second diagonal is:
d2 = 6.5 cm

Conclusion:
Hence, the length of the second diagonal of the rhombus is (8 - √5) cm, which matches with option 'D'.
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Area of rhombus is (7 + 6.5√5) cm2 and length of its one diagonal is (3 + 2√5) cm, then what is the length of its second diagonal?a)(8 + √5) cmb)(6 - 2√5) cmc)(8 + 3√5) cmd)(8 - √5) cmCorrect answer is option 'D'. Can you explain this answer?
Question Description
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