Question

The lenght of a rectangular shaped label is 1cm more than twice the breath. The perimeter is 110cm.find the area of rectangle​

Answer 1

Answer:

Let the width/breadth of the rectangular label be "x".

Then, its length

= 1 more than twice width

= 1 + 2 × x

= 2x + 1

Then, the perimeter of the label -

= 2 (length + breadth)

= 2 [(2x + 1) + x]

= 2 (2x + 1 + x)

= 2 (3x + 1)

= 6x + 2

But, the perimeter of the label = 110 cm (as given in question)

Then,

6x + 2 = 110

=> 6x = 110 - 2

=> 6x = 108

=> x = 108/6

=> x = 18

Hence, the width of the rectangular label = x = 18 cm

And, length of the rectangular label

= 2x + 1

= 2 × 18 + 1

= 36 + 1

= 37 cm

Now, area of the rectangular label

= length × breadth

= 18 × 37

= 666 cm²

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Answer 2

Explanation:

let let breadth of a rectangle label be =x

then it's length

1 + 2× x

2 x + 1

then the parameter of label

2(length + breath)

2[(2x+1)+x)]

2(2x+1+x)

2(3x+1)

6x+2

but, the parameter of label=110cm

then

6x+2=110

6x=110-2

6x=108

x=108/6

x=18

hence the the breadth of rectangular label=x=18cm

length of rectangular label=2x+1

2×18+1

36+1

37cm

now,

area of rectangular label =(l×b)

18×37

666cm