Question

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,440 ft. Determine the​ flag's width and length if the length is 340 ft greater than the width.

Answer 1

To find the width and length of the flag based on the given information, we can set up a system of equations.

Let:
- \( w \) = width of the flag (in feet)
- \( l \) = length of the flag (in feet)

According to the problem, we have two pieces of information:

1. The perimeter of the flag is 2,440 feet.
2. The length is 340 feet greater than the width.

We can express the perimeter \( P \) of a rectangle (which is what the flag essentially is) with the formula:
\[
P = 2l + 2w
\]

From the first piece of information:
\[
2l + 2w = 2440
\]
We can simplify this equation by dividing everything by 2:
\[
l + w = 1220 \quad \text{(Equation 1)}
\]

From the second piece of information:
\[
l = w + 340 \quad \text{(Equation 2)}
\]

Now we can substitute Equation 2 into Equation 1:
\[
(w + 340) + w = 1220
\]
This simplifies to:
\[
2w + 340 = 1220
\]
Next, we'll isolate \( w \):
\[
2w = 1220 - 340
\]
\[
2w = 880
\]
\[
w = 440 \quad \text{(Width)}
\]

Now we'll use the width to find the length using Equation 2:
\[
l = w + 340 = 440 + 340 = 780 \quad \text{(Length)}
\]

Thus, the dimensions of the flag are:
- Width = 440 feet
- Length = 780 feet

To verify, we can check the perimeter:
\[
P = 2l + 2w = 2(780) + 2(440) = 1560 + 880 = 2440 \text{ feet}
\]
This matches the given perimeter, confirming our solution.

**Final answer**: Width = 440 ft, Length = 780 ft.