Question

The width of a rectangle is 4 inches greater than half the length. The perimeter is 56 inches. What is the length and the width of the rectangle

Answer 1

length = 16 inches and width = 12 inches

Explanation:

Let l be the length and w be the width of the rectangle.

It is given that width is 4 inches greater than half of the length:

`w=(l)/(2)+4` ------1

Perimeter of the rectangle is given by
`2*(l+w)`

`2*(l+w)=56`

`l+w=28` ----------------2

Substituting w from equation 1 in equation 2, we get:

`l+(4+(l)/(2))=28`

`(3l)/(2)=24`

∴ l = 16 inches

Putting l=16 in equation 1, we get w=12.

Hence w= 12 inches.

Answer 2

Length of the rectangle = 16 inches

Width of the rectangle = 12 inches

Explanation:

Let the length of the rectangle be represented by x.

Then width can be expressed as
`\[(x)/(2)+4\]`

Perimeter of a rectangle is the sum of four sides of the rectangle.

This can be expressed as 2*(length + breadth)

=
`\[2* (x + (x)/(2)+4)\]`

=
`\[2* ((3x)/(2)+4)\]`

=
`\[3x + 8\]`

But perimeter is given as 56.

So,
`\[3x + 8 = 56\]`

=>
`\[3x = 48\]`

=>
`\[x = 16\]`

Hence length of the rectangle = 16 inches

Width of the rectangle =
`\[(16)/(2)+4\]` = 12 inches