Question

Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.

• A. None of the above
• B. 9 cm , 12 cm​
• C. 15 cm , 20 cm​
• D. 24 cm , 32 cm​

Answer 1

The correct option is D 24 cm , 32 cm​


Let STUV be the parallelogram.
Ratio of two adjacent sides of a parallelogram is 3 : 4.
Let the common multiple be x.
ST = 3x cm and TU = 4x cm
$\Rightarrow$ST = UV = 3x cm
$\Rightarrow$TU = SV = 4x cm …..(i)
[Opposite sides of a parallelogram]

Perimeter of STUV = 112 [Given]
$\Rightarrow$ST + TU + UV + SV = 112
$\Rightarrow$3x + 4x + 3x + 4x = 112 [From (i)]
$\Rightarrow$14x = 112
$\Rightarrow$x = 112/14
$\Rightarrow$x = 8
$\Rightarrow$ST = UV = 3x = 3 x 8 = 24 cm
$\Rightarrow$ TU = SV = 4x = 4 x 8 = 32 cm [From (i)]

∴ The lengths of the sides of the parallelogram are 24 cm, 32 cm, 24 cm and 32 cm.