Question

The length of a rectangle is four meters less than twice its width. If the perimeter of the rectangle is 100 meters, what is the width?
A) 32m
B) 8m
C) 24m
D) 18m

Answer 1

Let the width of the rectangle be \( w \) meters. According to the problem, the length \( l \) can be expressed in terms of the width as follows:

\[
l = 2w - 4
\]

The formula for the perimeter \( P \) of a rectangle is given by:

\[
P = 2(l + w)
\]

We know from the problem that the perimeter is 100 meters, so we can set up the equation:

\[
2(l + w) = 100
\]

Dividing both sides by 2 gives:

\[
l + w = 50
\]

Now we can substitute the expression for length \( l \) into the equation:

\[
(2w - 4) + w = 50
\]

Combining like terms:

\[
3w - 4 = 50
\]

Next, we add 4 to both sides:

\[
3w = 54
\]

Now, divide both sides by 3:

\[
w = 18
\]

The width of the rectangle is \( 18 \) meters. Therefore, the correct answer is:

**D) 18m**