Question

The length of a rectangle is 3 meters greater than 2 times the width. The perimeter of rectangle is 30 meters. What is the length of the rectangle?

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:

\[
l = 2w + 3
\]

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

\[
P = 2l + 2w
\]

We know the perimeter is 30 meters, so we can set up the equation:

\[
2l + 2w = 30
\]

Dividing the entire equation by 2 to simplify:

\[
l + w = 15
\]

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

\[
(2w + 3) + w = 15
\]

Combining like terms:

\[
3w + 3 = 15
\]

Next, we subtract 3 from both sides:

\[
3w = 12
\]

Now, we divide by 3:

\[
w = 4
\]

Now that we have the width, we can find the length using the expression for \( l \):

\[
l = 2(4) + 3 = 8 + 3 = 11
\]

Thus, the length of the rectangle is:

\[
\boxed{11} \text{ meters}
\]

To confirm, let's check the perimeter with these dimensions:

\[
P = 2l + 2w = 2(11) + 2(4) = 22 + 8 = 30 \text{ meters}
\]

The calculations are consistent, confirming that the length is indeed \( \boxed{11} \) meters.