Question

10.The area of a trapezium is 385 cm2 . Its parallel sides are in the ratio 3 : 4 and the perpendicular distance between them is 11 cm. Find its longer side.

Answer 1

Let the common multiple be x

• 1st parallel side = 3x
• 2nd parallel side = 4x

• Distance between them = 11 cm
• Area of a trapezium = 385 cm²

Area of a trapezium = (Sum of parallel sides × Distance between them)/2

Thus, 385 cm² = {(3x + 4x) × 11 cm}/2

or, 385 cm² = 77x /2

or, 385 cm² × 2 = 77x

or, 770 cm² = 77x

or, x = 770/77

x = 10 cm

1st parallel side = 3 × 10 = 30 cm

2nd parallel side = 4 × 10 = 40 cm

Longer side = 40 cm ✔️

Answer 2

Solution:

The parallel sides of the trapezium are in the ratio 3 : 4 .

Let them be 3x and 4x cm respectively .

Now the perpendicular distance between these two sides is given as 11 cm .

Area of s trapezium is given by :

=> ½ × [ Sum of parallel sides ] × [ Perpendicular distance ]

=> ½ × [ 3x + 4x ] × 11

=> ½ × 11 × 7x

This is equal to 385 cm²

So ,

½ × 11 × 7x = 385

=> 11 × 7x = 385 × 2

=> 77x = 385 × 2

=> x = 5 × 2

=> x = 10 cm .

Longer side = 4x = 40 cm .

This is the required answer .

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