Question

the ratio of two sides of parallelogram are in ratio 3 is to 4 and the perimeter is 42 cm find all the sides of the parallelogram​

Answer 1

AnswEr :

$\normalsize\bullet\sf\ let \: the \: first \: side(S_1) \: be \: 3x \: cm$

$\normalsize\bullet\sf\ let \: the \: second \: side(S_2) \: be \: 4x \: cm$

$\underline{\dag\:\textsf{According \: to \: given \: in \: question:}}$

$\normalsize\ : \implies{\boxed{\sf{Perimeter_{\parallel gm} = 2(S_1 \: + \: S_2) }}} \\ \\ \normalsize\ : \implies\sf\ 42 = 2(3x + 4x) \\ \\ \normalsize\ : \implies\sf\ 42 = 2(7x)$

$\normalsize\ : \implies\sf\ 42 = 14 x \\ \\ \normalsize\ : \implies\sf\ x = \frac{42}{14} = 3$

$\normalsize\ : \implies{\boxed{\sf \red{Value \: of \: x = 3}}}$

$\underline{\dag\:\textsf{Block \: the \: values \: in \: available \: data:}}$

$\:\:\normalsize\bullet\:\sf\ Side \: 1 \: = 3x \: cm$

$\normalsize\ : \implies\sf\ 3x = 3 \times\ 3$

$\normalsize\ : \implies\sf\color{darkblue}\ Side \: 1 = 9cm$

$\:\:\normalsize\bullet\:\sf\ Side \: 2 \: = 4x \: cm$

$\normalsize\ : \implies\sf\ 4x = 4 \times\ 3$

$\normalsize\ : \implies\sf\color{darkblue}\ Side \: 2 = 12cm$

Some Important related to it :

$\setlength{\unitlength}{0.83cm}\begin{picture}(12,4)\thicklines\put(7,8.9){ A }\put(12.6,8.9){ D }\put(5.6,5.9){ B }\put(11.2,5.9){ C }\put(5.4,7.5){ side\:1 }\put(8,5.6){ side\:2 }\put(6,6){\line(1,0){5}}\put(7.5,9){\line(1,0){5}}\put(12.5,9){\line(-1,-2){1.5}}\put(6,6){\line(1,2){1.5}}\end{picture}$

★Properties of Parallelogram :

• Opposite sides are equal.

• Opposite angles are equal.

• Diagnols bisect one another.

Answer 2

$\bold{\huge{\underline{\underline{\rm{Answer:}}}}}$

Four sides are of parallelogram are :

1. 9 cm
2. 12 cm
3. 9 cm
4. 12 cm

Given :

• The ratio of two sides of a parallelogram are 3:4
• Perimeter of the parallelogram = 42 cm

To Find :

• Sides of the parallelogram.

Solution :

Let x be the common multiple of the ratio 3:4.

•°• $\sf{Side_1}$ = 3x

$\sf{Side_2}$ = 4x

Perimeter of the sides = 42 cm

Formula :

$\bold{\large{\boxed{\red{\boxed{\mathtt{Perimeter\:=\:2\:(length\:+\:breadth)}}}}}}$

Block in the available data,

➞ $\mathtt{42\:=\:2(3x+4x)}$

➞ $\mathtt{42\:=\:6x\:+\:8x}$

➞ $\mathtt{42\:=\:14x}$

➞ $\mathtt{\dfrac{42}{14}\:=\:x}$

➞ $\mathtt{3\:=\:x}$

Substitute x = 3 in the ratio of sides.

$\bold{\large{\boxed{\blue{\mathtt{Side_1= 3x = 3 \times 3 = 9 cm. </p><p>}}}}}$

$\bold{\large{\boxed{\blue{\mathtt{Side_2= 4x = 4 \times 3 = 12 cm. </p><p>}}}}}$

Property of parallelogram :

• Opposite sides are parallel and congruent.

$\bold{\large{\boxed{\green{\mathtt{Side_3= 3x = 3 \times 3 = 9 cm}}}}}$

$\bold{\large{\boxed{\green{\mathtt{Side_4= 4x = 4 \times 3 = 12 cm}}}}}$