Question

a rectangular park is 140 meters long and 90 meters wide. give the length and width of another rectangular park that has the same perimeter but a smaller area. width = \\(\square\\) meters length = \\(\square\\) meters

Explanation:

Step1: Calculate original perimeter

The perimeter of a rectangle is $P = 2(l + w)$. Substitute $l=140$, $w=90$:
$P = 2(140 + 90) = 2(230) = 460$ meters

Step2: Define new rectangle variables

Let new width = $w'$, new length = $l'$. From perimeter: $2(l' + w') = 460$, so $l' + w' = 230$, or $l' = 230 - w'$.

Step3: Choose width to reduce area

Original area: $140 \times 90 = 12600$ m². To get smaller area, pick a width further from the square side (since square maximizes area for fixed perimeter). Choose $w' = 80$ meters.

Step4: Calculate new length

$l' = 230 - 80 = 150$ meters

Step5: Verify new area

New area: $150 \times 80 = 12000$ m², which is less than 12600 m².

Answer:

width = 80 meters
length = 150 meters

Note: Any pair where $l' + w' = 230$ and the values are not 140 and 90 (and not equal to each other, as that would be a square with maximum area) is valid, e.g., width=70, length=160 also works.