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.

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.

RELATED: