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Question

The two parallel sides and the distance between them are in the ratio 3:4:2 . If the area of the trapezium is 175cm, find its height.


Solution

let the two parallel sides of the trapezium be 3x and 4x and height be 2x.

area of the trapezium = 175cm²

therefore 1/2×h(b1+b2) = 175cm²

=> 1/2×2x(3x+4x) = 175cm²

=> x×7x = 175cm²

=> 7x² = 175cm²

=> x² = 175/7

=> x² = 25

=> x = √25

=> x = 5

hence parallel sides are 3x and 4x.

→ 3x = 3×5
= 15cm

→ 4x = 4×5
= 20cm

→ height of the trapezium = 2x
= 2×5
= 10cm

VERIFICATION:-

area of the trapezium = 1/2×h(b1+b2)

= 1/2×10(15+20)

= 5×35

= 175cm²

hence verified
 

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