Question

The length of a rectangle is 4 feet less than 2 times the width. If the perimeter is 82 feet, find the length and the width of the rectangle

Answer 1

length = 26 ft

width = 26 ft

Step-by-step explanation:

The length of the rectangle is 4 less than 2 times the width:

`length=2* width-4`

The perimeter of the rectangle is 82 ft:

`2*(length+width)=82`

Now let us substitute the value of length from the first equation into the second equation. This gives,

`2*(2* width-4+width)=82`

For convenience, let us represent the width by the letter w. This turns our equation into the following.

`\begin{gathered} 2*(2* w-4+w)=82 \\ \Rightarrow2(2w-4+w)=82 \end{gathered}`

since 2w + w = 3w, the above becomes

`2(3w-4)=82`

dividing both sides by 2 gives

`3w-4=(82)/(2)`
`3w-4=41`

adding 4 to both sides gives

`\begin{gathered} 3w=41+4 \\ 3w=45 \end{gathered}`

Finally, dividing both sides by 3 gives

`w=45/3`
`\boxed{w=15.}`

Hence, the width of the rectangle is 15 ft.

With the value of the width in hand, we now find the length of the rectangle.

`length=2* width-4`

since width = 15, the above equation gives

`\begin{gathered} length=2*15-4 \\ \Rightarrow length=30-4 \end{gathered}`
`\Rightarrow\boxed{length=26.}`

Hence, the length of the rectangle is 26 ft.

To summerise,

length = 26 ft

width = 26 ft