Question

Question #3021b

Answer 1

`W = 11/5`

Explanation:

Given:

The perimeter of a rectangle is 12:

`2L + 2W = 12`

`L + W = 6" [1]"`

The length of the rectangle is five less than 4 times the width:

`L = 4W-5`

Substitute into equation [1]:

`4W-5 + W = 6`

`5W = 11`

`W = 11/5`

Answer 2

`"width "=2.2`

Explanation:

`"let the width of the rectangle "=x`

`"then length "=4x-5`

`• " perimeter "=(2xx"width ")+(2xx"length")`

`rArr12=2x+2(4x-5)`

`rArr12=2x+8x-10`

`rArr10x-10=12larr" reversing the equation"`

`"add 10 to both sides"`

`10xcancel(-10)cancel(+10)=12+10`

`rArr10x=22`

`"divide both sides by 10"`

`(cancel(10) x)/cancel(10)=22/10`

`rArrx=22/10=11/5=2.2`

`"width "=x=2.2`

`"length "=4x-5=(4xx2.2)-5=8.8-5=3.8`