Math question - ( for a 5th Grade student)?

Question

Cedric has 52 feet of wood to use to make a RECTANGULAR garden. He wants the garden to have the greatest possible area. What dimensions should it have ???

** you guys i reaaaaaaaaaaaaaaaly need your help on this 1. its for my baby sister and im terrible in maths... HELP! ;(

Answer 1

its a square with 13 feet sde.

If a proof is to be sumbitted ask her her to find are at different side lenghts,

1,12
2,11
......
......
.......
13,13

14,2 etc and hence conclude.

I i dont know a better proof for fifth grader. otherwise i will nedd to use maxima minima or a quadratic equation atleast to prove that


sorry i cant help much



bythe way you dont adjust anything like 13.00001 or 12.9999999

square is a special case of rectangle with length=breadth

Answer 2

Four sides in a rectangle: A B C and D.
It must be rectangular, so two sides need to be equal, and the other two sides need to be equal. A=C and B=D

(A+B) + (C+D) needs to be 52 feet
C=A and D=B, thus: (A+B) + (A+B) = 52
2 * (A+B) = 52
(A+B) = 26

The surface of a rectangle is A*B.

Try all combinations of A+B if you want. You will find that the best combination is: A=B

{A,B} = {13,13} : surface 13*13 = 169 sq.ft
{A,B} = {12.5, 13.5} : surface 12.5*13.5 = 168.75 sq.ft
{A,B} = {12,14} : surface 12*14 = 168 sq.ft
{A,B} = {11,15} : surface 11*15 = 165 sq.ft
(and so on, becoming smaller each time)

You don't need to try {A,B} = {14,12} because A*B equals B*A

Thus A=13 and B=13
Because A=C and B=D, all sides are 13 feet.

Why is it the best combination if all sides are equal? This is because it resembles a circle the best. A circle has the largest surface for a given circumreference. In three dimensions, this would be a sphere, for instance a soap bubble. Similarly, a box with equal sides holds the largest volume (if it needs to be a box, not a sphere).

Answer 3

Length and width have to add up to 26 since 2•length + 2•width = perimeter, and length times width = area, so try some out.

1•25 = 25
2•24 = 48
3•23 = 69
.....
12•14 = 168
13•13 = 169

clearly, the rectangle with the largest area for a given perimeter is a square.

Answer 4

12 by 14

Answer 5

A square gives the maximum area, with each side being 13 feet. Since you want a rectangle, you could choose a rectangle closest to a square. Say 12 feet by 14 feet. Or, if fractions are allowed, 12.9999 feet by 13.0001 feet, or something like that.

Answer 6

for a given perimeterthe square has the greatest area
dimensions are 13 ft per side

Answer 7

13 by 13 square
A square is a rectangle.
A = 169 ft^2

Answer 8

just divide it by 4, so then its 13, then just make two of them 12 and the other 14

Answer 9

Im in 9th class but I think I could help.Divide the no.of feet of wood (52) by 4 equal sides and then arrange the arith...............................