Question

The perimeter of a parallelogram is 50 cm. One side is one and half times the other. The sides of the parallelogram are *
Plz answer

Answer 1

Longest side = 16.6 cm

Smaller side = 8.3

Let the longest side be X

Other side = X/2

Perimeter = 2X (L+B)

50 = 2 X (x+x/2)

50 = 2 X 3x/2

50 = 3x

x = 16.6

x/2 = 8.3

Answer 2

Given: Perimeter of Parallelogram = 50 cm

And, One side is one and half times the other.

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To find: Measure of the sides of Parallelogram?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

☯ Let's consider one side of Parallelogram be x cm.

Therefore, Othe side of Parallelogram will be (1½ of x) cm = 3/2 x cm.

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⋆ DIAGRAM:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\put(-0.2,2.3){ \sf 1\frac{1}{2}x\:\:cm }\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\put(3,0.5){\sf x cm}\end{picture}$

⠀⠀⠀

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Perimeter_{\;(parallelogram)} = 2(a + b)}}}}$

Here,

$\sf We\:have \begin{cases} & \sf{a = \bf{x\: cm}} \\ \\ & \sf{b = \bf{\dfrac{3}{2}\:cm}} \\ \\ & \sf{Perimeter = \bf{50\:cm}} \end{cases}$

$\dag\;{\underline{\frak{Putting\:values\:in\:formula,}}}$

$:\implies\sf 50 = 2 \bigg(x + \dfrac{3}{2} x \bigg)\\ \\ \\ :\implies\sf 50 = 2 \bigg( \dfrac{2x + 3x}{2}\bigg)\\ \\ \\ :\implies\sf 50 = \cancel{2} \times \dfrac{5x}{ \cancel{2}}\\ \\ \\ :\implies\sf 50 = 5x\\ \\ \\ :\implies\sf x = \cancel{\dfrac{50}{5}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 10}}}}}\;\bigstar$

Therefore,

• One side of Parallelogram, x = 10 cm
• Other side of Parallelogram, 3/2 x = 3/2 × 10 = 15 cm

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:The\:side\:of\: parallelogram\:are\: {\textsf{\textbf{10\:cm\:and\;15\:cm}}}.}}}$