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

Answer:

length = 26 ft

width = 26 ft

Explanation:

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

$length=2\times width-4$

The perimeter of the rectangle is 82 ft:

$2\times(length+width)=82$

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

$2\times(2\times width-4+width)=82$

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

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

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

$2(3w-4)=82$

dividing both sides by 2 gives

$3w-4=\frac{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.

$length=2\times width-4$

since width = 15, the above equation gives

$\begin{gathered} length=2\times15-4 \\ \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