Question

The length of a rectangular shaped label is 1 cm more than twice the width .The perimeter is 110 cm .Find the area of rectangle?

Answer 1

We can set up the formula:

2L +2W = 110

We can also set up length as 2x+1 and width as x so plug this in:

2(2x+1)+2x=110

Expanded to:

4x+2+2x=110

 

Rewritten as:

6x=108

Divide both sides by 6:

x=18

So width is 18 cm  

and length is 37 cm

Answer 2

$<b>Heya mate. (^_-). Solution below.$
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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.

$<marquee>Hence, the area if the rectangular label is 666 cm².</marquee>$
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Thank you.. ;-)