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In a parallelogram, the length of one diagonal is twice of the other diagonal. If its area is 50 sq m. then the length of its bigger diagonal is.
Answers
Answer:
Given the diagonals p,q of a parallelogram, its area is
[ABCD]=12pqsinθ,
where θ is the angle between diagonals, i.e. the area takes the largest possible value in the case of rhombus (θ=π2).
In this case assuming p>q we have:
14p2=50⟹p=102–√.
However this is the smallest possible value of p, i.e. varying θ you can construct a parallelogram of area 50 for any value of p≥102–√.
Answer:
Given the diagonals p,q of a parallelogram, its area is
[ABCD]=12pqsinθ,
where θ is the angle between diagonals, i.e. the area takes the largest possible value in the case of rhombus (θ=π2).
In this case assuming p>q we have:
14p2=50⟹p=102–√.
However this is the smallest possible value of p, i.e. varying θ you can construct a parallelogram of area 50 for any value of p≥102–√.