Question

A rectangular room is 6 meters longer than it is wide, and its perimeter is 32 meters. How do you find the dimension of the room?

Answer 1

Length is 11 m.; Width is 5 m.

Explanation:

Define:
`color(white)("XX")L = " length"`
`color(white)("XX")W = " width"`

Given
`color(white)("XX")L=W+6`
`color(white)("XX")"(perimeter = " = 2(L+W) = 32`

`color(white)("XX")rarr 2((W+6)+W) = 32`

`color(white)("XX")rarr 2W+6 = 16`

`color(white)("XX")rarr W=5`

and since `L=W+6`
`color(white)("XX")rarr L=11`

Answer 2

5m x 11m

Explanation:

take the width of the room as `x`, then the length of the room becomes `x+6` according to the data.

i can take these data and write an equation as follows which shows the perimeter of the room

`32 = 2(x+6) + 2x`
`32 =4x+ 12`
`4x= 20`
`x= 5m` this is the width of the room

the length of the room = `5+ 6 = 11m`

so the dimensions of the room :
5m x 11m