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.

9514 1404 393

  a) 2(L+W)=420; L-W=110

  b) length: 160 ft; width: 50 ft

Step-by-step 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 ...

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.

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.)

the answer to this question is 3/19

step-by-step explanation: