Answered

Please help me 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.

Verified Answer :

Dannymal

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!

Edmund

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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