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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

User Serverfaces
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1 Answer

21 votes
21 votes

Answer:

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

User Malki
by
2.4k points