Question

length of a rectangle is 4meters less than twice it's breadth.if the perimeter of the rectangle is 52 meter find its length and breadth​

Answer 1

★ Given :-

The Length of a rectangle is 4m less than twice it's Breadth. The perimeter of the rectangle is 52m.

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★ To Find :-

Length and Breadth of the rectangle

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★ Used Formula :-

$\color{navy}⇢\: \red{ \boxed{ \bf Perimeter \: _{(Rectangle)} = 2 \: (Length + Breadth )}}$

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★ Solution :-

Here,

The Length of a rectangle is 4m less than twice it's Breadth.

So,

• Breadth = x
• Length = 2x-4

The perimeter of the rectangle is 52m.

$\color{navy}⟹ \: \red{ \bf Perimeter \: _{(Rectangle)} = 2 \: (L + B)}$

Where,

• Length = L
• Breadth = B

Now,

$⟹ \bf \: Perimeter \: _{(Rectangle)} = 2 \: (L + B)$

$⟹ \: \bf 52m= 2 \: (2 x - 4 + x)$

$⟹ \: \bf 52= 2 \: (3x - 4 )$

$⟹ \: \bf 52= 6x - 8$

$⟹ \: \bf 52 + 8= 6x$

$⟹ \: \bf 60= 6x$

$\displaystyle⟹ \: \bf \cancel\frac{60}{6} = x$

$\red{⟹ \: \underline{ \boxed{ \bf \: x = 10}}}$

∴ Breadth = x = 10

∴ Length = 2x-4 = 2×10-4 = 20-4 = 16

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★ Verification :-

$⟹ \bf \: Perimeter \: _{(Rectangle)} = 2 \: (L + B) \:$

$⟹ \bf \: 52= 2 \: (16+ 10)$

$⟹ \bf \: 52= 2 \: (26)$

$⟹ \: \boxed{ \bf \: 52= 52}$

Hence, verified !

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Answer 2

Answer :

• Length of rectangle is 16m
• Breadth of rectangle is 10m

Given :

• length of a rectangle is 4m less than twice it's breadth.
• The perimeter of the rectangle is 52m

To find :

• its length and breadth

Solution :

Given,

• length of a rectangle is 4meters less than twice it's breadth then,

• Let breadth of rectangle be x
• Let the length of rectangle be 2x - 4

Given,

• Perimeter of rectangle is 52m

We know that

• Perimeter of rectangle = 2(l + b)

Where,

• l is length of rectangle
• b is breadth of rectangle

↦ Perimeter of rectangle = 2(length + breadth)

↦ 52 = 2(2x - 4 + x)

↦ 52 = 2(3x - 4)

↦ 52 = 6x - 8

↦ 6x = 52 + 8

↦ 6x = 60

↦ x = 60/6

↦ x = 10

Finding the length and breadth of rectangle :

↦ Length of rectangle = 2x - 4

↦ Length of rectangle = 2(10) - 4

↦ Length of rectangle = 20 - 4

↦ Length of rectangle = 16m

Length of rectangle is 16m.

↦ Breadth of rectangle = x

↦ Breadth of rectangle = 10m

Breadth of rectangle is 10m

Hence,

• Length of rectangle is 16m
• Breadth of rectangle is 10m

Verification :

↦ Perimeter of rectangle = 2(l + b)

↦ 52 = 2(16 + 10)

↦ 52 = 2(26)

↦ 52 = 52

Hence , Verified.