Question

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 480 feet. Determine the​ flag's length and width if the length is 60 feet greater than the width. Use pencil and paper. Write three situations to which you could apply the resulting system of equations.

Answer 1

Let x be the width of the flag in feet. Then the length of the flag is x + 60 feet. The perimeter of the flag is the sum of the lengths of its four sides, which is:

2(x + x + 60) = 4x + 120 feet

Setting this equal to 480 feet, we have:

4x + 120 = 480

Solving for x, we get:

4x = 360

x = 90

Therefore, the width of the flag is 90 feet and the length is 150 feet.

Three situations to which this system of equations could be applied are:

A farmer wants to plant a rectangular field of flowers. He knows the perimeter of the field but needs to determine the length and width in order to calculate the area and decide how many flowers to buy.

A carpenter wants to build a rectangular frame for a painting. She knows the perimeter of the frame but needs to determine the length and width in order to calculate the amount of wood needed and the cost.

A city planner wants to design a rectangular park. She knows the perimeter of the park but needs to determine the length and width in order to calculate the area and decide how many trees and benches to place in the park.