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.



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:
[tex]P=2W+2L[/tex]
[tex]P=130m+210m[/tex]
[tex]P=340m[/tex]
Then, let's get the area of the bigger one:
[tex]A=WL[/tex]
[tex]A=65m*105m[/tex]
[tex]A=6825m^2[/tex]

Then let's try using a rectangle with a smaller ratio:
[tex]P=100m+240m[/tex]
[tex]P=340m[/tex]
Then:
[tex]A=50m*120m[/tex]
[tex]A=6000m^2[/tex]

If you used a square:
[tex]P=170+170[/tex]
[tex]P=340[/tex]
[tex]A=WL[/tex]
[tex]A=85^2[/tex]
[tex]A=7225[/tex]

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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