Question

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,100 Determine the flag's width and length if the length is 410 ft greater than the width.

Answer 1

The perimeter of the flag, which is a rectangle, is equal to twice the length plus twice the width:

$P=2l+2w$

Let "w" represent the width of the rectangle. If the length is 410ft greater than the width, you can express the length as follows:

$l=w+410$

Replace the expression above in the formula of the perimeter:

$P=2(w+410)+2w$

You know that the perimeter is P= 2,100ft, then:

$2100=2(w+410)+2w$

The next step is to solve for w:

- Distribute the multiplication on the parentheses term:

$\begin{gathered} 2100=2\cdot w+2\cdot410+2w \\ 2100=2w+820+2w \\ \end{gathered}$

- Order the like terms together and simplify:

$\begin{gathered} 2100=2w+2w+820 \\ 2100=4w+820 \end{gathered}$

- Subtract 820 to both sides of the equal sign

$\begin{gathered} 2100-820=4w+820-820 \\ 1280=4w \end{gathered}$

- Divide both sides by 4

$\begin{gathered} \frac{1280}{4}=\frac{4w}{4} \\ 320=w \end{gathered}$

Now that the width is determined, you can calculate the length of the flag:

$\begin{gathered} l=w+410 \\ l=320+410 \\ l=730 \end{gathered}$

The width of the flag is 320ft and the length is 730ft