Question

The perimeter of a rectangle is 40 m. The length of the rectangle is 4 m less than 5 times its breadth. Find the length of the rectangle.
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Answer 1

Answer :

• Length of rectangle is 16m

Given :

• The perimeter of a rectangle is 40m
• The length of the rectangle is 4m less than 5 times its breadth

To find :

• Length of rectangle

Solution :

To find the length of rectangle, we need to use the formula of perimeter of rectangle

• Let the breadth of rectangle be x

Given, the length of the rectangle is 4m less than 5 times its breadth then,

• 5x - 4

• Let the length of rectangle be 5x - 4

We know that,

• Perimeter of rectangle = 2(l + b)

Where ,

• l is length
• b is breadth

Given, perimeter of rectangle is 40m

➞ Perimeter of rectangle = 2(length + breadth)

➞ 40 = 2(5x - 4 + x)

➞ 40 = 10x - 8 + 2x

➞ 40 = 12x - 8

➞ 12x = 40 + 8

➞ 12x = 48

➞ x = 48/12

➞ x = 4

• Breadth of rectangle = 4m

Finding the Length of rectangle :

➞ 5x - 4

➞ 5(4) - 4

➞ 20 - 4

➞ 16 m

Hence , Length of rectangle is 16m

Verification :

• Perimeter of rectangle = 2(l + b)

Where,

• Length = 16m
• Breadth = 4m
• Perimeter = 40m

➞ Perimeter of rectangle = 2(l + b)

Taking RHS,

➞ 40 = 2(16 + 4)

➞ 40 = 2(20)

➞ 40 = 40

LHS = RHS

Hence verified

Answer 2

Answer:

Let breadth be x, then 5x - 4 = length

Perimeter = 2( l +b)

=> 40 = 2(l + b)

=>40  = 2(5x - 4 + x)

=> 40 = 12x - 8

=> 12x  = 40+ 8

=> 48÷12 = 4

So length  = 5*4 = 20-4 = 16 m

∴ length = 16 m