Question

The perimeter of a rectangle is 60 cm. If the length of a rectangle is 5 times its breadth find its dimensions

Answer 1

Given

Perimeter of a Rectangle is 60cm

Length of a Rectangle is 5 times its breadth

To Find

Dimensions of Rectangle

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Perimeter of a Rectangle=2(length+breadth)

According to the question:-

Let the breadth of a Rectangle be 'x'

Then length be 5×x=5x

Perimeter of Rectangle=2(x+5x)

=>60=2(6x)

=>12x=60

=>x=60÷12

=>x=5

Breadth of Rectangle ='x'=5cm

Length of a Rectangle=5x=5×5=25cm

∴Dimensions of Rectangle is :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ length=25cm

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ breadth=5cm

CHECK:-

Perimeter of Rectangle=2(25+5)

Perimeter of Rectangle=2(30)=60cm

Extra information=>

Perimeter is the total distance occupy by a solid 2D figure around its edge.

Example in Real life : To fence a field with wire we need to find the cost of fencing in such case perimeter will used because we have to only fence border of the field.

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Answer 2

Given :-

• Shape = Rectangle
• The Perimeter of Rectangle = 60cm
• The length of a rectangle is 5 times its breadth.

To Find :-

• Dimensions of the Rectangle.

Solution :-

Let the Breadth of the Rectangle be x cm

Then Length of the Rectangle = 5x cm

According to the Question :

⟹ Perimeter of Rectangle = 2 ( L + B )

⟹ 60 = 2 ( 5x + x )

⟹ 60 ÷ 2 = 5x + x

⟹ 30 = 5x + x

⟹ 30 = 6x

⟹ 30 ÷ 6 = x

⟹ 5 = x

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Therefore :-

• Length of Rectangle = 5x = 5 × 5 = 25cm
• Breadth of Rectangle = x = 5 cm

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★ Additional Info :

Formulas Related to Rectangle :

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

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