The length of a rectangle is twice its breadth If the perimeter is 72 m then find the length and

breadth of the rectan

2 thoughts on “The length of a rectangle is twice its breadth If the perimeter is 72 m then find the length and <br /><br />breadth of the rectan”

1. [tex]\large\sf\underline{Given\::}[/tex]

   • Length of a rectangle is twice it’s breadth

   • Perimeter of the rectangle = 72 m

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   [tex]\large\sf\underline{To\:find\::}[/tex]

   • The length of the rectangle

   • The breadth of the rectangle

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   [tex]\large\sf\underline{Creating\:the\:road\:map\:for\:Solution\::}[/tex]

   In the question we are given that the length of a rectangle is twice it’s breadth and the Perimeter of the rectangle is given as 72 m. So at first we will assume some value for breadth. Twice of the assumed value will be the length of the rectangle. After that we would equate the given value of perimeter and the formula of the perimeter with the substituited assumed value . Doing so we will end up getting our final answers. Let’s proceed !

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   [tex]\large\sf\underline{Assumption\::}[/tex]

   Let the :

   • Breadth of the rectangle be x m.

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   According to the question :

   • Length of the rectangle = 2 × b = 2 × x = 2x m.

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   [tex]\large\sf\underline{Formula\:to\:be\:used\::}[/tex]

   • Perimeter of the rectangle = [tex]\sf\:2(l+b)[/tex]

   where :

   • l stands for Length

   • b stands for breadth

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   [tex]\large\sf\underline{Solution\::}[/tex]

   Let’s substitute the assumed value in the formula :

   [tex]\sf\:Perimeter\:=\:2(2x+x)—(i)[/tex]

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   According to the question :

   • Perimeter of the rectangle = 72 m —(ii)

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   Now equating (i) and (ii) :

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   [tex]\sf\leadsto\:2(2x+x)=72[/tex]

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   • Multiplying the terms in LHS

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   [tex]\sf\leadsto\:4x+2x=72[/tex]

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   • Adding the terms in LHS

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   [tex]\sf\leadsto\:6x=72[/tex]

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   • Transposing 6 to the other side

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   [tex]\sf\leadsto\:x=\cancel{\frac{72}{6}}[/tex]

   [tex]\small\fbox\red{★\:x\:=\:12\:m}[/tex]

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   Now substituting the value of x in assumed value :

   • Length of the rectangle = 2 × x = 2 × 12 = [tex]\small{\underline{\boxed{\mathrm\orange{\:24\:m}}}}[/tex]

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   • Breadth of the rectangle = x = [tex]\small{\underline{\boxed{\mathrm\orange{\:12\:m}}}}[/tex]

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   !! Hope it helps !!

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2. Given :–

   • Length of the rectangle = 2 × Breadth

   This can also be written as

   〔l = 2b〕

   Where:

   ‍l is the length

   b is the breadth

   To find :–

   ★ Length of the rectangle = ?

   ★ Breadth of the rectangle = ?

   Solution :–

   Here, we apply the formula of perimeter of rectangle.

   Perimeter of rectangle = 2 (l + b)

   ⇒ Perimeter of rectangle = 2 (2b + b)

   ⇒ 72 = 2 × 3b

   ⇒ 72 = 6b

   ⇒ b = 72 ÷ 6

   ⇒ b = 12

   ∴ The Breadth of rectangle = 12 m

   For finding the value of length, we shall substitute the value of breadth in the above mentioned equation that is

   l = 2b

   ⇒ l = 2 × 12

   ⇒ l = 24 cm

   ∴ The Length of rectangle = 24 m

   Reply