Question

a rectangular field is 60 yards wide and 100 yards long. give the length and width of another rectangular field that has the same perimeter but a smaller area. width = \\(\square\\) yards length = \\(\square\\) yards

Explanation:

Step1: Calculate original perimeter

The perimeter of a rectangle is $P=2(l+w)$. Substitute $l=100$, $w=60$:
$P=2(100+60)=2\times160=320$ yards

Step2: Set new rectangle parameters

Let new width $w'=50$ yards. Use $P=2(l'+w')$ to find $l'$:
$320=2(l'+50)$
$l'+50=\frac{320}{2}=160$
$l'=160-50=110$ yards

Step3: Verify area comparison

Original area: $A=100\times60=6000$ square yards
New area: $A'=110\times50=5500$ square yards, which is smaller.

Answer:

width = 50 yards
length = 110 yards

Note: Any pair where $l'+w'=160$ and the difference between $l'$ and $w'$ is greater than 40 (the difference in the original rectangle) will work, e.g., 40 yards and 120 yards is also a valid solution.