Question

4.
The ratio between the adjacent sides of a
parallelogram is 3:5. The perimeter of the
parallelogram is 144 cm. Find the lengths of the
sides of the parallelogram.



please give me the answer step by step
​

Answer 1

GivEn ratio between the adjacent sides of a parallelogram is 3:5.

And, The perimeter of the parallelogram is 144 cm.

We have to find, the lengths of the sides of the parallelogram.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Let sides of Parallelogram be 3x and 5x.

⠀⠀⠀⠀⠀⠀⠀

⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,3)\qbezier(3,0)(3,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(0,0)(0,0)\put(-0.3,-0.2){ \sf A }\put(-0.3,1.5){5x}\put(3.1,-0.2){ \sf B }\put(1.1,-1){3x}\put(4,3){ \sf C }\put(0.7,3){ \sf D }\end{picture}$

⠀⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{We\;know\;that,}}}$

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\purple{Perimeter_{\;(parallelogram)} = 2( side_1 + side_2)}}}}$

⠀⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{Putting\;values\;:}}}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 2(3x + 5x) = 144$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 2(8x) = 144$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 16x = 144$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf x = \cancel{ \dfrac{144}{16}}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\pink{\;9\;}}}}}\;\bigstar$

━━━━━━━━━━━━━━━━━━━━━━

Therefore,

Sides of Parallelogram are,

• $\sf side_1 = 3x = 3 \times 9 = 27\;cm$

• $\sf side_1 = 3x = 5 \times 9 = 45\;cm$