Question

The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram.

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• The perimeter of a parallelogram is 72
• The width of the parallelogram is 4 meters less than its length

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• The length and the width of the parallelogram

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Length of parallelogram = x
• width of parallelogram = y

[ ★ Perimeter of parallelogram = Sum of all sides ]

By first condition :-

(The perimeter of a parallelogram is 72 )

➠ ( x + x + y + y ) = 72

➠ 2(x + y ) = 72

➠ (x + y) = 72/2

➠ (x + y) = 36 ............(1)

Second condition :-

( The width of the parallelogram is 4 meters less than its length )

➠ y = x - 4

➠ x - y = -4 ..............(2)

_________________________

Add equation (1) and (2)

➠ 2x = 32

➠ x = 32/2

➠ x = 16

_________________________

Again, keep value of x in equ(1)

➠ ( 16 + y ) = 36

➠ y = 36 - 16

➠ y = 20

____________________________

Thus:-

• Length of parallelogram = 16 m
• width of parallelogram = 20 m

$\large{\underline{\underline{\mathfrak{\bf{\blue{Answer\:Verification}}}}}}$

Check first condition :-

(The perimeter of a parallelogram is 72 )

★ 2( Length + width ) = 72

➠ 2( 16 + 20 ) = 72

➠ 2 × 36 = 72

➠ 72 = 72

L.H.S. = R.H.S.

that's proved

___________________________

Answer 2

• $\huge\orange{\underline\textbf{Given...}}$

✰✰ The perimeter of the parallelogram is 72 m...

• $\huge\orange{\underline\textbf{To find...}}$

✰✰ The length and the width of the parallelogram...

• $\huge\orange{\underline\textbf{Solution...}}$

✰✰ Let the length be x...

✰✰ Let the width be y...

( We know that perimeter is the sum of all sides... )

So,

➪ x + x + y + y = 72 m

➪ 2x + 2y = 72

➪ 2 ( x + y ) = 72

➪ x + y = $\dfrac{72}{2}$

➪ $\green{\underline\textbf{x + y = 36}}$⠀⠀⠀⠀ ⠀ --⠀⠀ ⠀⠀⠀eq 1...

The, sum of length and width will be 36 m...

Now,

( The width of the parallelogram is 4 m less than its length... )

➪ y = x - 4

➪ $\green{\underline\textbf{x - y = - 4}}$⠀⠀⠀⠀ ⠀ --⠀⠀ ⠀⠀⠀ eq 2...

Adding both equations...

• x + y = 36
• x - y = - 4

⠀⠀⠀-⠀ +⠀⠀ +⠀ ⠀⠀ ⠀⠀⠀

⠀⠀____________

⠀⠀ 2y = 40

⠀⠀____________

➪ y = 40 / 2

➪

✪ $\boxed{\green{\underline\textbf{ y = 20}}}$

Substituting value of y in eq 1...

➪ x + y = 36

➪ x + 20 = 36

➪

✪ $\boxed{\green{\underline\textbf{x = 16}}}$⠀⠀ ⠀ ⠀⠀ ⠀

Therefore, length will be 16m and width will be 20m...

_______________________

$\red{\underline\textbf{Verification...}}$⠀⠀

➪ x + x + y + y = 72 m

➪ 2x + 2y = 72

➪ 2 ( x + y ) = 72

➪ 2 ( 16 + 20 ) = 72

➪ 2 × 36 = 72

✪ $\boxed{\blue{\underline\textbf{72 = 72}}}$

Hence, verified...