Question

Ｔｗｏ ａｄｊａｃｅｎｔ ｓｉｄｅｓ ｏｆ ａ ｐａｒａｌｌｅｌｏｇｒａｍ ａｒｅ ｉｎ ｔｈｅ ｒａｔｉｏ ２：３ ａｎｄ ｉｔｓ ｐｅｒｉｍｅｔｅｒ ｉｓ ５０ｃｍ ．Ｆｉｎｄ ｔｈｅ ｓｉｄｅｓ ｏｆ ｔｈｅ ｐａｒａｌｌｅｌｏｇｒａｍ​

Answer 1

$\large\mathbb \blue{\fcolorbox{blue}{black} { \ HERE\ IS\ YOUR\ ANSWER \ }}$

SOLUTION

We Know That

• Opposite Side of Parallelogram is equal.
• Let say the Ratio of side are 2x & 3x

Perimeter of the parallelogram is 50 cm.

Perimeter = 2 (length+base)

⠀⠀⠀⠀⠀⠀⠀⠀⠀ 50 = 2 (2x+3x)

⠀⠀⠀⠀⠀⠀⠀⠀⠀ 50 = 2(5x)

⠀⠀⠀⠀⠀⠀⠀⠀⠀ 50 = 10x

⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = 50/10

⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = 5 cm

Now the sides are :-

• 2x = 2×5 = 10 cm
• 3x = 3×5 = 15 cm

Hence, the side of Parallelogram is 10 cm & 15 cm.

Answer 2

Given : Two adjacent sides of a parallelogram are in ratio 2 : 3 & Perimeter of parallelogram is 50 cm.

To Find : Find the sides of Parallelogram ?

_________________________

Solution : Let x be the common in given ratio.

$~$

• $\leadsto$Length of Parallelogram = 2x
• $\leadsto$Breadth of Parallelogram = 3x

$~$

$\underline{\frak{As~ we ~know~ that~:}}$

• Opposite sides of a parallelogram are equal so other two adjacent sides will be same.

$~$

◗Perimeter of Parallelogram = Sum of its all sides

$\qquad{\sf:\implies{50~=~2x~+~2x~+~3x~+~3x}}$

$\qquad{\sf:\implies{50~=~4x~+~6x}}$

$\qquad{\sf:\implies{50~=~10x}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{50}{10}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{x~=~5}}}}}$★

$~$

Therefore,

• Length = 2x => 2(5) = 10 cm
• Breadth = 3x => 3(5) = 15 cm.

$~$

Hence,

$\therefore\underline{\sf{The~two~ adjacent ~sides ~of ~the ~Parallelogram ~are ~\bf{\underline{10 ~cm ~\& ~15 ~cm}}}}$