Question

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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 = 50 yards
length = 150 yards

Explanation:

Step1: Calculate original perimeter

The perimeter of a rectangle is $P=2(l+w)$. For the original field:
$P=2(100+60)=2\times160=320$ yards

Step2: Set new rectangle constraints

Let new width = $w$, new length = $l$. We need $2(l+w)=320$, so $l+w=160$. Area $A=l\times w$ must be less than original area ($100\times60=6000$ square yards).

Step3: Choose valid dimensions

Pick $w=40$ yards. Then $l=160-40=120$ yards. Check area: $120\times40=4800$ square yards, which is less than 6000.

Answer:

width = 40 yards, length = 120 yards
*(Note: Any pair where $l+w=160$ and $l
eq w$, with the product $l\times w < 6000$ is valid; this is one example.)*