Question

The perimeter of a rectangle is 48m. The width of the rectangle is 2 more than half the length. Find the length and the width.

Answer 1

The Length of the rectangle is 14
`(2)/(3)` m and width 9
`(1)/(3)` m.

Explanation:

Given,

Perimeter of the rectangle = 48 m

The width of the rectangle is 2 more than half the length.

To find the length and width of the rectangle.

Formula

Perimeter of the rectangle of length l and width b is = 2(l+b)

Let,

Length = l

Width =
`(l)/(2) +2` [ given]

Now,

According to the problem

2(l+
`(l)/(2) +2` ) = 48

or,
`l+(l)/(2) +2` = 24

or,
`(3l)/(2)` = 24-2

or,
`(3l)/(2)` = 22

or, l =
`(22X2)/(3)` =
`(44)/(3)` = 14
`(2)/(3)`

And width =
`(44)/(3X2)+2` =
`(28)/(3)` = 9
`(1)/(3)`

Hence,

Length = 14
`(2)/(3)` m and width = 9
`(1)/(3)` m

Answer 2

l = 14 2/3

w = 9 1/3

Explanation:

Let l = length

w = 2+ 1/2l

We know the perimeter is 48 and is given by

P = 2(l+w)

48 = 2(l + 2 +1/2l)

Distribute

48 = 2l+4+l

Combine like terms

48 = 3l +4

Subtract 4 from each side

48-4 = 3l+4-4

44= 3l

Divide each side by 3

44/3 = 3l/3

44/3 =l

14 2/3 =l

Now we need to find w

w = 2 + 1/2 l

=2 + 1/2(44/3)

= 2 +44/6

=12/6 +44/6

=56/6

=9 1/3