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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