Two sides of a parallelogram are in the ratio 4:3. If its perimeter is $56 cm,$ then what are the lengths of its sides?

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16cm, 16cm, 16cm, and 16 cm

16cm, 12cm, 16cm, and 12 cm

12cm, 12cm, 12cm, and 12 cm

16cm, 14cm, 16cm, and 14 cm

answer is B.

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Detailed Solution

It is given that the ratio of the sides of the parallelogram is 4:3.
Let two sides be

4 x and 3 x .

The perimeter of a parallelogram is the sum of all its sides.
Given that the perimeter of the parallelogram is 56 cm.

∴ Perimeter = 4 x + 3 x + 4 x + 3 x ⇒ 56 = 4 x + 3 x + 4 x + 3 x ⇒ 56 = 14 x

⇒ x = 5614 ⇒ x = 4

∴ 4 x = 4 × 4 = 16 and 3 x = 3 × 3 = 12

Therefore, the lengths of the two sides of a parallelogram are 16cm and 12cm.
We know that parallelogram is a quadrilateral in which two opposite sides and two opposite angles are equal.
Therefore, the lengths of its sides are 16cm, 12cm, 16cm, and 12cm.
Hence option (2) is correct.

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