Question

$\huge \sf \green {Question}$

The lengths of the parallel sides of a trapezium are in the ratio 5 : 6 and the distance between them is 12 cm. Find the length of each of its parallel sides if the area of the trapezium is 330 cm'.



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Answer 1

Answer:

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Step-by-step explanation:

let the length of the 2 parallel side be 5x and 6x.

height = 12 cm

area= 330 cm2

= 1/2 x h (a+b)

= 1/2 x 12 (5x + 6x ) = 330

= 6 x 11x = 330

= 11x = 330/6= 55

x = 55/11=5

therefore,

area of first parallel side = 5x = 5 x 5 = 25 cm

area of second parallel side = 6x = 6 x 5 = 30 cm

Answer 2

Given:

Length of parallel sides are in ratio 5:6

Distance between two parallel sides = 12cm

Area of trapezium = 330cm²

Answer:

Let the common ratio be x

So, the parallel sides of trapezium are 5x and 6x

$Area = \\ \frac{1}{2} (Sum \: of \: parallel \: sides)× (height)$

So,

$330 = \frac{1}{2} (5x + 6x)(12) \\ \\ 330 = \frac{1}{2} \times 11x \times 12 \\ \\ 330 = 11x \times 6 \\ \\ 11x = \frac{330}{6} \\ \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5$

So, Parallel sides of the trapezium is 25cm and 30cm.

[Now refer the attachment]

In right ∆ABE

(Using Pythagoras theorem)

AB² = AE² + BE²

AB² = 2.5² + 12²

AB² = 6.25 + 144

AB² = 150.25

AB = √150.25

AB = 12.25 cm

Therefore,

All sides of the required trapezium are 25cm, 30cm, 12.25cm & 12.25cm

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