Question

1. 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.

Explanation:

Step1: Define variables

Let $w$ = width (ft), $l$ = length (ft)

Step2: Write perimeter equation

Perimeter of rectangle: $2l + 2w = 420$

Step3: Write length-width relation

Length is 110 ft longer than width: $l = w + 110$

Step4: Substitute $l$ into perimeter eq

Substitute $l = w + 110$ into $2l + 2w = 420$:
$2(w + 110) + 2w = 420$

Step5: Simplify and solve for $w$

Expand and combine like terms:
$2w + 220 + 2w = 420$
$4w + 220 = 420$
$4w = 420 - 220$
$4w = 200$
$w = \frac{200}{4} = 50$

Step6: Calculate length $l$

Use $l = w + 110$:
$l = 50 + 110 = 160$

Answer:

a. System of equations:
$2l + 2w = 420$
$l = w + 110$
b. Width = 50 feet, Length = 160 feet