Question

Two sides of a parallelogram are in the ratio 5:3. If its perimeter is 64 cm, find the lengths of its sides?

Option 1: 20 cm and 12 cm
Option 2: 15 cm and 9 cm
Option 3: 25 cm and 15 cm
Option 4: 30 cm and 18 cm

Answer 1

The lengths of the sides of a parallelogram with a perimeter of 64 cm and sides in the ratio 5:3 are 20 cm and 12 cm, corresponding to Option 1.

Step-by-step explanation:

To find the lengths of the sides of a parallelogram with sides in the ratio 5:3 and a perimeter of 64 cm, you can set up the following equation: 2(5x + 3x) = 64, where 5x and 3x are the lengths of the sides of the parallelogram. Solving for x gives us:

2(8x) = 64

16x = 64

x = 4

Now, we calculate the lengths of the sides:

Length of one side = 5x = 5(4) = 20 cm

Length of the adjacent side = 3x = 3(4) = 12 cm

Therefore, the lengths of the sides are 20 cm and 12 cm, which corresponds to Option 1.