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The difference between two parallel sides of a trapezium is $4 cm$ . The perpendicular distance between them is $19 cm$ . If the area of the trapezium is $475 cm 2$ Find the length of the parallel sides.

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26 cm, 22cm

24cm, 27cm

29cm, 20cm

27 cm,23cm

answer is D.

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Detailed Solution

Let's assume that the two parallel sides of the trapezium are

“ a ” c m

and

“ b ” c m

, respectively,
Given that the difference between the trapezium's two parallel sides is

4 cm

⇒ a − b = 4 … (1)

Distance between the two lines,

h = 19 cm

Area of the trapezium,

A = 475 cm 2

We know that Area,

A = 12 h (a + b)

Put values in the equation above:

⇒ 475 = 12 × 19 × (a + b)

The term in a division shifts to the multiplication, that is, it shifts from the denominator to the numerator, and vice versa.

⇒ 475 × 2 19 = (a + b)

Simplify the equation above:

⇒ 25 × 2 = (a + b) ⇒ 50 = (a + b)

Writing the equation again:

⇒ a + b = 50 … (2)

Combining equations (1) and (2)

2 a = 54

When the term in the multiplication switches sides, the division follows.

⇒ a = 542 ⇒ a = 27 cm

Place value of

a

in the equation now (1)

⇒ a − b = 4 ⇒ 27 − b = 4

The symbol of the phrases also changes when they are transferred from one side to another. Negative changes become positive, while positive changes become negative.

⇒ 27 − 4 = b ⇒ b = 23 cm

The lengths of the parallel sides are therefore

27 cm

and

23 cm

, respectively, and this is the necessary response.
Thus, the right response is 27 cm and 23 cm.

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