Question

9. In a trapezium, the two parallel sides and the distance between them are in the
ratio 3: 4: 2. If the area of the trapezium is 175 cm”, find the lengths of the parallel
sides.
D​

Answer 1

Answer:

Let the two parallel sides and the distance between them be 3x, 4x, 2x cm respectively

Area = `1/2` (sum of parallel sides) x (distance between parallel sides)

= `1/2` (3x + 4x) x 2x = 175 (given)

=> 7x x x = 175

=> 7x2 = 175

=> x2 = 25

=> x = 5

Height i.e. distance between parallel sides = 2x = 2 x 5 = 10 cm

Step-by-step explanation:

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Answer 2

Answer:

Let the lengths of the parallel sides of the trapezium be 3acm and 4acm. Let the height of the trapezium or the distance between them be 2acm.

Area of a trapezium =

2

1

×(Sumofparallelsides)×height

=>

2

1

×(3a+4a)×2a=175cm

2

=>

2

1

×7a×2a=175

a

2

=25

=>a=5

Hence, the height of the trapezium =2a=10cm