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?(1 point)
Responses

8m


32m


18m


24m

Answer 1

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

\[
l = 2w - 4
\]

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

\[
P = 2l + 2w
\]

Substituting the expression for the length into the perimeter formula gives:

\[
100 = 2(2w - 4) + 2w
\]

Now, let's simplify and solve for \( w \):

\[
100 = 4w - 8 + 2w
\]

Combine like terms:

\[
100 = 6w - 8
\]

Add 8 to both sides:

\[
108 = 6w
\]

Now, divide both sides by 6:

\[
w = 18
\]

So, the width of the rectangle is \( 18 \) meters.

The correct response is:

**18m**