Question
In a trapezium, the two non parallel sides are equal in length, each being 5 units. The parallel sides are at a distance of 3 units apart. If the smaller side of the parallel side is of length 2 units, then what is the sum of the diagonals of the trapezium ?
Hint:
As the Non parallel sides are equal then it is an isosceles trapezium.
In isosceles trapezium length of diagonals are equal. Given height = 3 units
Smaller of parallel sides = 2 units ,length of non parallel sides = 5 units
The correct answer is: 6√5 units
Ans :- 
Explanation :-
Draw perpendicular lines from C and D to AB which intersects at F and E
respectively. Given height = 3 units .we get a rectangle DCFE and EF = 2.
Step 1:- Find lengths of AE and FB
By applying pythagoras theorem in ΔADE and ΔBFC
Step 2:- Find the length of diagonal AC
Consider ΔACF , AF = AE +EF = 4+2 = 6 units
CF = 3 units
By applying pythagoras theorem ,
Step 3:- Find the length of diagonal BD
As the diagonals are equal in isosceles trapezium
AC = BD
BD = 
Sum of diagonals = AC+BD = + =
Sum of lengths of diagonals of trapezium = .
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