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Answers
Answer:
Length of AB is 5 unit & length of AD is 5√3 unit.
Perimeter is 5 + 5√3 + 5 + 5√3 = 10( 1 + √3 ) unit.
Step-by-step explanation:
Let the point ( where diagonals intersect each other at 90° ) be O.
Since AB = BC & AD = DC,
Area of BAD = Area of BCD { ∆s are congruent }
In ∆BAD,
= > tangent of /_ ABD = tan60° = √3
= > AD / AB = √3
= > √3 AB = AD
= > √3 BC = CD
Thus,
= > Area of figure = 25√3 unit^2
= > 2 x area of BCD = 25√3 unit^2 { area of BAD + area of BCD = 2 x area of BCD, since both are equal, seen at the starting }
= > 2 x 1 / 2 x BC x CD = 25√3 unit^2
= > BC x CD = 25√3
= > BC x √3 BC = 25√3 { from above }
= > BC = 5
Therefore, √3 BC = √3 x 5 = 5√3 = CD
Hence,
Length of AB is 5 unit & length of AD is 5√3 unit.
Perimeter is 5 + 5√3 + 5 + 5√3 = 10( 1 + √3 ) unit.
*a free hand figure is provided.
Use
Trigonometry
Congruence of Triangle
Let
AB = a
AD = b
BD = c
Area of Triangle = 25 ( root 3 ) / 2
(since two triangles are congruent by RHS congruence )
Area = 1/2 * base * height
= 1/2 * a * b................ (1)
(since a and b are perpendicular)
= 1/2 * AD sin 30° * BD
= 1/2 * b * 1/2 * c..........(2)
= 1/2 * AB sin 60° * BD
= 1/2 * a * (root 3) / 2 * c.......(3)
From (2) and (3)
1/2 * a * (root 3) / 2 * c = 1/2 * b * 1/2 * c
a * (root 3) = b.......... (4)
Put value of b from (4) in (1)
1/2 * a * ( a * (root 3) ) = 25 ( root 3 ) / 2
a ^2 = 25
a = 5
AB = a = 5
b = a * ( root 3 )
= 5 ( root 3 )
AD = b = 5 ( root 3 )
I hope you know how to get to the perimeter
In my Opinion the above answer by @ abhi @ maths aryabhatta is more suitable and easy
But I provided a new approach so it's too correct