Question

The length of a rectangle is 1 unit less than twice a number. Its width is 2 units more than the same number.The perimeter of the rectangle is 36 units.​

Answer 1

Given data : The length of a rectangle is 1 unit less than twice a number. Its width is 2 units more than the same number.The perimeter of the rectangle is 36 units.

To find : Find the length and breadth of the rectangle.

Solution : Let, the number be x.

Now, a/c to given data,

➜ Length of the rectangle, L = (2x - 1) units ----{1}

➜ Breadth of the rectangle, B = (x + 2) units ----{2}

➜ Perimeter of the rectangle = 36 units ----{3}

Here, we know, formula perimeter of rectangle,

➜ Perimeter of the rectangle = 2 * {length + breadth}

[from eq. {1}, {2} and {3}]

➜ 36 = 2 * {(2x - 1) + (x + 2)}

➜ 36 = 2 * {2x - 1 + x + 2}

➜ 36 = 2 * {2x + x - 1 + 2}

➜ 36 = 2 * {3x + 1}

➜ 36 = 6x + 2

➜ 6x = 36 - 2

➜ x = 34/6

➜ x = 17/3 units

Now, put value of x in eq. {1}

➜ Length of the rectangle, L = (2x - 1)

➜ Length of the rectangle, L = (2 * 17/3 - 1)

➜ Length of the rectangle, L = 34/3 - 1

➜ Length of the rectangle, L = (34 - 3)/3

➜ Length of the rectangle, L = 31/3 units

Now, put value of x in eq. {2}

➜ Breadth of the rectangle, B = (x + 2)

➜ Breadth of the rectangle, B = (17/3 + 2)

➜ Breadth of the rectangle, B = (17 + 6)/3

➜ Breadth of the rectangle, B = 23/3 units

Answer : Hence, the length of the rectangle is 31/3 units and the breadth of the rectangle is 23/3 units.

{Verification :

➜ Perimeter Of The Rectangle = 2 * {length + breadth}

Put value of the length and the breadth

➜ P.O.T.R = 2 * {31/3 + 23/3}

➜ P.O.T.R = 2 * {54/3}

➜ P.O.T.R = 108/3

➜ P.O.T.R = 36 units

Hence it verified.}

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Answer 2

Answer:-

length=31, width=23

3 3

Step by step explanation:-

let the number be x and.

let the length be 2x-1 and the width be x+2.

perimeter=2(l+b)

36=2(2x-1 + x+2)

36=2(2x+x - 1+2)

36=2(3x+1)

36=6x+2

36-2=6x

6x=34

x=34

6

x=17

3

therefore, length=2x-1 =2×17-1=34-1=34-3=31

3 3 3 3

width=x+2=17+2=17+6=23

3 3 3

Proved:-

perimeter=2(l+b)

=2×31+23

3 3

=2×31+23

3

=2×54

3

=2×18

=36