With this. A rectangular field is
65
meters wide and
105
meters long.
Give the length and width of another rectangular field that has the same perimeter but a smaller area.

Well the L and the W could be 75 and 95
Because 75 + 75 + 95 + 95= 340
And 75 x 95= 7125
Same Perimeter, different Area

First, let’s get the perimeter of the rectangle:
$$P=2W+2L$$
$$P=130m+210m$$
$$P=340m$$
Then, let’s get the area of the bigger one:
$$A=WL$$
$$A=65m*105m$$
$$A=6825m^2$$

Then let’s try using a rectangle with a smaller ratio:
$$P=100m+240m$$
$$P=340m$$
Then:
$$A=50m*120m$$
$$A=6000m^2$$

If you used a square:
$$P=170+170$$
$$P=340$$
$$A=WL$$
$$A=85^2$$
$$A=7225$$

There you have it. A rectangle with a smaller area with the same perimeter.
What does it show? The smaller the difference you get from width and length, the larger the area is.

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