Question

original rectangle. Find the length and the breadth of the original rectands
The width of a rectangle is two-thirds its length. If the perimeter x 180 metres
dimensions of the rectangle.​

Answer 1

✰ AnSwer :

☯ Dimensions :

• Length = 54 cm
• Width = 36 cm

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✒ GiVen :

• Width of the rectangle is two - thirds its length.
• Perimeter of the rectangle = 180 cm.

✒ To Find :

• Value of Length and Width (dimensions)respectively.

✒ SoluTion :

• Let us assume the length of the rectangle be l.
• So, width of the rectangle = ⅔l

We know that,

$\implies$Perimeter of a rectangle = 2 (length + width)

$\implies$ 180 = 2 ( l + ⅔l )

$\implies$ 180 = 2 ( 3l + 2l /3 )

$\implies$ 180 = 2 ( 5l/3 )

$\implies$ 180 = 10l/3

$\implies$ l = 180 × 3/10

$\implies$ l = 54 cm

So,

• Length = 54 cm

Now, let us find width,

$\implies$ Width = ⅔l

$\implies$ Width = ⅔ × 54

$\implies$ Width = 36 cm

Hence,

• Width = 36 cm

Therefore, length and width of the rectangle are 54 cm and 36 cm respectively.

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✰ Verification :

As perimeter is given as 180 we can verify it by substituting the values of length and width.

$\implies$ Perimeter = 2 (l + w)

$\implies$ 180 = 2(54 + 36)

$\implies$ 180 = 2(90)

$\implies$ 180 = 180

$\implies$ LHS = RHS

☯ Hence verified!!

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Answer 2

$\sf{\underline{\boxed{\pink{\large{\mathfrak{Answer}}}}}}$

☆ Dimensions :

• Length = 54 cm
• Width = 36 cm

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{Given}}}}}}$

• Width of the rectangle is two - thirds its length.
• Perimeter of the rectangle = 180 cm.

$\sf{\underline{\boxed{\pink{\large{\mathfrak{To\: find}}}}}}$

• dimensions of the rectangle

$\sf{\underline{\boxed{\pink{\large{\mathfrak{Solution}}}}}}$

• Let the length be x
• Therefore , width = 2 / 3 x

$\sf{\underline{\boxed{\green{\large{\bold{ perimeter = 2 ( l + b )}}}}}}$

$\implies$ 180 = 2 ( x + 2 / 3x )

$\implies$ 180 = 2 ( 3x + 2x /3 )

$\implies$ 180 = 2 ( 5x/3 )

$\implies$ 180 = 10x/3

$\implies$ x = 180 × 3/10

$\implies$ x = 54 cm

So,

$\sf{\underline{\boxed{\green{\large{\bold{ length = 54cm}}}}}}$

Now,

$\implies$ Width = ⅔x

$\implies$ Width = ⅔ × 54

$\implies$ Width = 36 cm

Hence,

$\sf{\underline{\boxed{\green{\large{\bold{ width = 36cm }}}}}}$

Therefore,

$\sf{\underline{\boxed{\purple{{\bold{ length = 54cm \: and \: width = 36cm }}}}}}$

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