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 answer

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

\[ l = 2w - 4 \]

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

\[ P = 2l + 2w \]

Given that the perimeter is 100 meters, we can write the equation:

\[ 2l + 2w = 100 \]

Substituting for \( l \) from the earlier expression, we have:

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

Expanding this gives:

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

Combining like terms results in:

\[ 6w - 8 = 100 \]

Next, we can add 8 to both sides:

\[ 6w = 108 \]

Dividing both sides by 6 yields:

\[ w = 18 \]

Therefore, the width of the rectangle is:

\[ \boxed{18 \text{ meters}} \]

To verify, we can calculate the length:

\[ l = 2w - 4 = 2(18) - 4 = 36 - 4 = 32 \]

Now, let's check the perimeter:

\[ P = 2l + 2w = 2(32) + 2(18) = 64 + 36 = 100 \]

The calculated perimeter is indeed 100 meters, confirming that the width of the rectangle is correct at:

\[ \boxed{18 \text{ meters}} \]