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Q.

The adjacent sides of a parallelogram are in the ratio of $2 : 3$ , and its perimeter is 20 cm. Determine the length of its adjacent sides.

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a

4cm, 6cm

b

2cm, 3cm

c

6cm, 9cm

d

8cm, 12cm

answer is A.

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Detailed Solution

Given, the adjacent sides of a parallelogram are in the ratio of

2 : 3

, and its perimeter is 20 cm.
Let the adjacent sides of a parallelogram be 2x and 3x as per the given ratio.
Then, by the property of opposite sides being equal for any parallelogram, the remaining two sides will also be 2x and 3x.
Thus, we have, the diagram of the parallelogram as follows,
Question Image

Question Image

Now, we know that the perimeter of any two-dimensional figure is the sum of the side lengths of all its sides, so using this fact, we have, the perimeter of the given parallelogram as follows,

2 x + 3 x + 2 x + 3 x = 20 10 x = 20 x = 2010 x = 2

So, we have, the lengths of the adjacent sides as follows,

2 x = 2 × 2 = 4

cm

3 x = 3 × 2 = 6

cm
Hence, the correct option is (1).

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