Question

The area of a trapezium is 384 sq cm. Its parallel sides are in the ratio 5:3 and the distance between

them is 12 cm. Find the sides of the trapezium.​

Answer 1

Answer:

Area of the trapezium =384 cm

2

The parallel sides are in the ratio 3:5 and the perpendicular height between them is 12cm.

Suppose that the sides are in x multiples of each other.

Then, length of the shorter side =3x

Length of the longer side =5x

Area of a trapezium =

2

1

×(Sum of parallel sides)×( Height)

⇒384=

2

1

×(3x+5x)×(12)

⇒384=

2

12

×(8x)

⇒384=6×(8x)

⇒8x=

6

384

=64

⇒x=

8

64

=8 cm

∴ Length of the shorter side =3×x=3×8=24 cm

And, length of the longer side =5×x=5×8=40 cm

Differnece between the length is 16 cm