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
Glad to Help!

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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