Question

In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units and height of the trapezium is 10 units, what is the length of diagonal BD?​

Answer 1

Answer:

√136 units

Step-by-step explanation:

In trapezium ABCD, AB || CD and AC = BD. If area of the trapezium is 60 sq units and height of the trapezium is 10 units, what is the length of diagonal BD?​

Area of Trapezium = (1/2)(AB + CD) * height

=> 60 = (1/2)(AB + CD) * 10

=> AB + CD = 12

AE⊥CD & BF⊥CD  

DE = CF ( as AC = BD)

AB * 10 + (1/2)DE * 10 + (1/2)CF * 10  = 60

=> AB + DE = 6

BD² = 10² + (AB + DE)²

=> BD² = 100 + 6²

=> BD² = 136

=>BD = √136 units