Question

a rectangular field is 130 meters long and 90 meters wide. give the length and width of another rectangular field that has the same perimeter but a larger area. width = meters length = meters

Explanation:

Step1: Calculate the original perimeter

$P = 2\times(130 + 90)=2\times220 = 440$ (meters)

Step2: Recall the property of rectangle area

For a rectangle with a fixed perimeter, the closer the length and width are to each other, the larger the area. The original rectangle has length - width difference of $130 - 90=40$ meters. We want a rectangle with the same perimeter and a smaller length - width difference. Let the length be $l$ and the width be $w$, and $2(l + w)=440$, so $l + w = 220$. We can choose $l = 120$ and $w = 100$.

Answer:

width = 100 meters
length = 120 meters