Question

The Perimeter of a Parallelogram ABCD is 140cm. If one of the sides is greater than the other by 10 cm , find the lengths of all the sides of the parallelogram.​

Answer 1

The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm.

Let smaller side (a) =x then longer side

(b)=x+10

Perimeter =2(a+b)=2(x+x+10)=140

Smaller side =30cm Larger side =30+10=40 cm => x=30

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The Perimeter of a Parallelogram ABCD is 140cm. If one of the sides is greater than the other by 10 cm , find the lengths of all the sides of the parallelogram.

$\large\underline{ \underline{ \sf \maltese{ \: Diagram:- }}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

$\large\underline{ \underline{ \sf \maltese{ \:Given:- }}}$

• Perimeter of the Parallelogram = 140cm
• One is greater then the other by 10 cm

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find\::- }}}$

• The Lengths of all the sides of the Parallelogram.

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

Let AB be greater than BC by 10cm in the Parallelogram ABCD ( diagram ) and say BC is x cm long.

$\qquad \quad {:} \longrightarrow \sf{\bf{ BC \: = \: x }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ </strong><strong>AB</strong><strong> \: = \: </strong><strong>x\</strong><strong>:</strong><strong> </strong><strong>+</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>0</strong><strong> }}$

$\underbrace\red{\boxed{ \sf \blue{The \: Opposite \: sides \: of \: a \: Parallelogram \: are \: Equal }}}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ BC \: = \: AD \: = \: x }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ DC \: = \: AB \: = \: x \: + \: 10}}$

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$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Situation :}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: AB \: + \: BC \: + \: CD \: + \: DA \: = \: Perimeter }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{(x + 10) \: \green + \: x \: \green+ \: (x + 10) \: \green + \: x \: = \: Perimeter }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{(x + 10) \: \green + \: (x + 10) \: \green + \: x \: \green + \: x \: = \: 140 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{4x \: + \: 20 \: = \: 140 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{4x \: = \: 140 \: - \: 20 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{4x \: = \: 120 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \frac{120}{4} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \cancel\frac{120}{4} }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{x \: = \: 30 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 30 }}}$

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• AB = x + 10 = 30 + 10 = 40cm
• BC = 30cm

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ AB \: = \: DC \: = \underline {\underline{ 40cm}}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ AD \: = \: BC \: = \underline {\underline{ 30cm}}}\\\end{gathered}\end{gathered}$

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More For Knowledge :-

$\underbrace\red{\boxed{ \sf \blue{Important \: Properties \: of \: a \: Parallelogram }}}$

• It's Opposite sides are equal.
• It's Opposite angles are equal.
• It's Diagonal bisect each other.
• It's Diagonals divide the Parallelogram into two Congruent Triangles

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