Question

Perimeter of a parallelogram is 100 cm. One of its
sides is less by 10 cm, than twice of the other side.
Find the lengths of all sides.​

Answer 1

★Given:-

• Perimeter of a parallelogram = 100 cm
• One of its  sides is less by 10 cm than twice of the other side.

★To find:-

• Length of all sides.

★Solution:-

Let one side of the parallelogram = x

Given that one of its  sides is less by 10 cm than twice of the other side.

Hence,

• The other side = 2x-10

Using the formula,

✦Perimeter of a parallelogram = 2(l+b)

We have,

• Perimeter = 100cm
• l = length = x
• b = breadth = 2x-10

Putting the values,

⇒Perimeter = 2(l+b)

⇒100 = 2(x + 2x-10 )

⇒100 = 2(3x-10)

⇒100 = 6x - 20

⇒120 = 6x

⇒x = 120/6

⇒x = 20cm

∴One side of parallelogram is 20cm.

Other side of parallelogram:-

⇒ 2x - 10

⇒ 2(20) - 10

⇒ 40 - 10

⇒ 30cm

Hence,the length's of sides of parallelogram are 20 cm & 30cm.

____________

Answer 2

$\begin{gathered}\bf{\underline{\underline{★ Given :-}}}\\\end{gathered}$

Perimeter of a parallelogram is 100 cm.

One of its sides is less by 10 cm, than twice of the other side.

$\begin{gathered}\bf{\underline{\underline{ ★ To\:find : - }}}\\\end{gathered}$

length of all sides.

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

It's given that the area of parallelogram is 100cm.

So , we can assume one of its as x and let the other be 2x - 10

( Given that One of its sides is less by 10 cm, than twice of the other side )

$\large{\boxed{\boxed{\sf{Solution : - }}}}$

$\sf\purple{Perimeter = 2 ( l + b ) }$

Puttung the values ,

$\tt{Perimeter \ = \ 2 ( x \ + \ ( 2x - 10) }$

$\tt{100 \ = \ 2 ( 3x - 10 ) }$

$\tt{100 \ = \ 6x - 20 }$

$\tt{120 \ = \ 6x }$

$\tt{x \ = \ 20cm}$

Therefore,

❛️️️️❛ x = 20cm ❜❜

❛️️️️❛ 6x - 10 = 30cm ❜❜

⟹ Length of two sides is 20 and 30 cm respectively.