Question

a and b are the two parallel sides and h is the altitude of a trapezium.If a : b: h:
3: 4 : 2 and the area of the trapezium is 28 cm", find a, b and h.
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Answer 1

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Answer 2

Given:

• a and b are the parallel sides of trapezium.
• h is the altitude of the trapezium.
• Ratio of a , b and h is 3 : 4 : 2
• Area of trapezium is 28 cm².

To Find:

• What is the measure of parallel sides and altitude of the trapezium?

Solution: Let x be the common in given ratio. Therefore,

• Side a = 3x
• Side b = 4x
• Altitude h = 2x

As we know that ➸

★ Area of trapezium = 1/2(sum of parallel sides ) x Distance between them

But, area of trapezium is 28 cm²

A/q

$\implies{\rm }$ 28 = 1/2 ( 3x + 4x ) $\times$ 2x

$\implies{\rm }$ 28 = 7x $\times$ x

$\implies{\rm }$ 28 = 7x²

$\implies{\rm }$ 28/7 = 7x²

$\implies{\rm }$ 4 = x²

$\implies{\rm }$ √2 x 2 = x

$\implies{\rm }$ 2 cm = x

Hence,

➪ Parallel sides are a = 3x = 3(2) = 6 cm

➪ b = 4x = 4(2) = 8 cm and

➪ altitude h = 2x = 2(2) = 4 cm .