Question

A seed company planted a floral mosaic of a national flag. The perimeter of the

rectangular planting area is 420 feet. The length of the area is 110 feet longer
than the width.

a.) Write a system of equations to relate the
length and width of the planting area.

b.) Use the system of equations to
determine the length and width of
the planting area.

Answer 1

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Answer:

a) 2(L+W)=420; L-W=110

b) length: 160 ft; width: 50 ft

Explanation:

The formula for the perimeter (P) in terms of length (L) and width (W) is ...

P = 2(L+W)

We can use this as one of the equations. The other will relate the length and width according to their difference:

L -110 = W

Substituting the given perimeter in the above equation, our system of equations is ...

• 420 = 2(L+W)
• L-110 = W

Substituting for W in the first equation gives ...

420 = 2(L +(L -110))

210 = 2L -110

320 = 2L

160 = L

160 -110 = W = 50

The planting area is 160 feet long by 50 feet wide.

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Comment on the question

Most national flags have a length/width ratio of 1.5 or 2. The flags of Vatican City and Switzerland are square (1.0). The longest flag is that of Qatar, with an aspect ratio of width:length = 11:28, about 2.545. The "national flag" described here has an aspect ratio of width:length = 5:16, or 3.2. Apparently, it is not to scale, or not from Earth. (The US flag aspect ratio is 1.9.)