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Mathematics

Two parallel sides of a trapezium are in the ratio 2 : 3 and the distance between them is 12 cm. If the area of the trapezium is 240 cm2; the length of its larger parallel side is :

  1. 16 cm

  2. 20 cm

  3. 24 cm

  4. 32 cm

Area Trapezium Polygon

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Answer

Given:

Two parallel sides of a trapezium are in the ratio 2 : 3.

The distance between the parallel sides = 12 cm.

The area of the trapezium = 240 cm2.

Let the parallel sides of a trapezium be 2a and 3a.

Two parallel sides of a trapezium are in the ratio 2 : 3 and the distance between them is 12 cm. If the area of the trapezium is 240 cm2; the length of its larger parallel side is : Area of a Trapezium and a Polygon, Concise Mathematics Solutions ICSE Class 8.

As we know, the area of a trapezium = 12\dfrac{1}{2} x (sum of parallel sides) x height

⇒ 12\dfrac{1}{2} x (2a + 3a) x 12 cm2 = 240 cm2

⇒ 12\dfrac{1}{2} x 5a x 12 = 240

⇒ 12\dfrac{1}{2} x 60a = 240

⇒ 30a = 240

⇒ a = 24030\dfrac{240}{30}

⇒ a = 8

So, the length of its larger parallel side = 3a

= 3 x 8 cm

= 24 cm

Hence, option 3 is the correct option.

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