it takes 80 feet of fencing to enlcose your garden. According to your calculations, you will need 350 square feet to plant everything you want. Is your garden big enough? Explain your answer! setup the problem and solve. Show me, Help me Please.
thank you so much to all who answerr
2007-12-06 12:21:17 · 5 answers · asked by miya 5 in Science & Mathematics ➔ Mathematics
The most "area to perimeter efficient" shape is a circle. This means that if you want 350sqFt, the shape that will have the smallest perimeter is a circle. Let's find the radius of a circle of area 350.
350=PIr^2
350/PI=r^2
sqrt(350/PI)=r
r=10.5550206 feet
The perimeter Circumference= 2PI*r
=2*PI*10.5550206
=66.3191504 feet.
You can enclose a 350 sq feet circle with about 66 feet. You DO have enough fencing.
2007-12-06 12:27:39 · answer #1 · answered by SaintPretz59 4 · 0⤊ 0⤋
Let x = 1st side
The other side:
= (80/2) - x
= 40 - x
Finding the 1st side:
x(40 - x) = 350
40x - x^2 = 350
x = 12.9289321881345
Finding the other side:
= 40 - 12.9289321881345
= 27.0710678118655
Answer: The dimension of the lot in order to contain exactly a 350 square feet plantation should be:
width = 12.9289321881345 feet
length = 27.0710678118655 feet
Proof 1 (perimeter):
= 2(12.9289321881345 + 27.0710678118655)
= 2(40)
= 80 feet
Proof 2 (area):
= 12.9289321881345 * 27.0710678118655
= 350 square feet
You may round the dimension to 13 by 27 feet where the area can be 351 square meters of an 80-perimeter lot.
Note: The most ideal dimension is 20 by 20 where the area is 400 square meters and can contain more than enough the
350 square meter requirement.
In a 20 by 20 the perimeter is 80 feet and the area is 400 square meters.
2007-12-06 13:29:03 · answer #2 · answered by Jun Agruda 7 · 3⤊ 0⤋
2x+2y=80
xy>350 y=40-x
so 40x-x^2>= 350
x^2-40x+350<=0
calculating the roots x= ((40+-sqrt(1600-1400))/2
x =20+-5*sqrt2 so any x as 20-5 sqrt 2 <= x <= 20+5sqrt 2
and the corresponding so x+y=40 would do it
2007-12-06 12:37:40 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
the rectangle with the largest area for a given perimeter is a square.
a 20x20 square has perimeter 80, area 400 ft².
2007-12-06 12:26:50 · answer #4 · answered by Philo 7 · 1⤊ 0⤋
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2016-10-19 11:24:06 · answer #5 · answered by holtzer 4 · 0⤊ 0⤋