Question

EXERCISE 18 A
1. The ratio of two sides of a parallelogram is 3:5. If the perimeter is 64 cm, find the length of
sides of the parallelogram.
Tafadrilateral are 90° 800 1250 and yo find the value of​

Answer 1

Explanation:

Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\put (4,4.2){\sf a\:cm}\put (6.5,2){\sf b\;cm}\end{picture}$

Given:-

The ratio of two sides of a parallelogram is 3:5.

perimeter of the parallelogram =64cm

To find:-

Length of sides

Solution:-

Let the sides be 3x and 5x

As we know that in a parallelogram

$\boxed {\sf Perimeter =2 (a+b)}$

• Where a and b are the sides of the parallelogram
• Substitute the values

$\\\qquad\qquad\displaystyle\sf {:}\longrightarrow 2 (3x+5x)=64$

$\\\qquad\qquad\displaystyle\sf {:}\longrightarrow 6x+10x=64$

$\\\qquad\qquad\displaystyle\sf {:}\longrightarrow 16x=64$

$\\\qquad\qquad\displaystyle\sf {:}\longrightarrow x=\dfrac {64}{4}$

$\\\qquad\qquad\displaystyle\sf {:}\longrightarrow x=16$

________________________________

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail 3x=3\times 4 =12cm$

$\\\qquad\qquad\displaystyle\sf {:}\rightarrowtail 5x=5\times 4=20cm$

$\\\\\therefore\sf Sides\:of\:the\:parallelogram \:are\:12cm\:and\:20cm.$

Answer 2

Given :

• Ratio of two sides of a parallelogram = 3 : 5
• The perimeter of parallelogram = 64 cm

To Find :

• The length of sides of the parallelogram

Solution :

Let the ratio constant be "x" . Then sides of paralleogram are 3x and 5x.

Perimeter of parallelogram is given by ,

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

Here ,

• a and b are adjacent sides of parallelogram

We have ,

• Perimeter = 64 cm
• a = 3x and b = 5x

Substituting the values ;

$\\ : \implies \sf \: 64\:cm = 2(3x + 5x)$

$\\ : \implies \sf \: 64 \:cm= 2(8x)$

$\\ : \implies \sf \: 64 \:cm= 16x$

$\\ : \implies \sf \: x = \frac{64\:cm}{16}$

$\\ : \implies{\underline{\boxed {\red{\mathfrak{x = 4 \: cm}}}}}$

Now ,

• a = 3x = 3(4) = 12 cm
• b = 5x = 5(4) = 20 cm

Hence ,

• The Length of sides of parallelogram are 12 cm and 20 cm.