Question

The ratio of 2 sides of a parallelogram is 3:4 and perimeter is 42 CM. Find the measure of all the sides

Answer 1

Question:

The ratio of two sides of a parallelogram is 3:4 and perimeter is 42 cm. Find the measure of all the sides.

Answer:

9 cm , 12 cm , 9 cm , 12 cm .

Note:

• A quadrilateral whose opposite sides are equal and parallel is called parallelogram.

• Both the diagonals of a parallelogram bisect each other.

• In a parallelogram, opposite angles are equal.

• In parallelogram, the sum of two adjacent angles is equal to 180°.

• If L is the longer side and B is the shorter side of a parallelogram, then its perimeter P is given by ; P = 2(L+B) .

Solution:

Let's assume a parallelogram ABCD with AB & CD as its longer sides and AD & BC as its shorter sides .

It is given that;

The ratio of two sides of a parallelogram is 3:4.

Thus,

Let AD = BC = 3x

and AB = CD = 4x .

Also;

According to the question, the perimeter of the parallelogram is 42 cm.

Thus;

=> P = 2(AB + BC)

=> 42 = 2(4x + 3x)

=> 42 = 2•7x

=> 42 = 14x

=> x = 42/14

=> x = 3 cm

Now,

AD = BC = 3x = 3•3 cm = 9 cm

AB = CD = 4x = 4•3 cm = 12 cm

Hence,

The sides of the parallelogram are ;

9 cm , 12 cm , 9 cm , 12 cm .

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given :

Sides of parallelogram are in ratio of 3:4 and Perimeter is 42 cm

_________________________

To Find :

Measure of its all the sides

_________________________

Solution :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{B}}\put(11.1,0.9){\large{C}}\put(9.9,2.1){\large{O}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(11,1){\line(-1,1){2}}\put(8,1){\line(2,1){4}}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\end{picture}$

• In ∆ BOC ; Using Pythagoras theorem :

• In ∆ BOC ; Using Pythagoras theorem :

If the sides are in ratio of 3:4

Then,

Take one side as 3x

and other side as 4x

As we know that Formula for perimeter of parallelogram is :

$\Large \leadsto {\boxed{\boxed{\sf{ \star Perimeter \: = \: 2(l \: + \: b)}}}}$

Put values

⇒Perimeter = 2(3x + 4x)

⇒42 = 2(7x)

⇒42 = 14x

⇒x = 42/14

⇒x = 3 cm

Then,

First side = 3x = 3(3) = 9 cm

Other side = 4x = 4(3) = 12 cm

So,

All the sides are 9cm, 12cm, 9cm, 12cm

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Additional Information :

• Parallelogram is a 2-D shape.

• It's parallel sides are equal.

• Diagonal bisects each other.

• Formula for Perimeter of Parallelogram is 2(l + b)