Answered

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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.

Sagot :

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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