Question

Among all rectangles that have a perimeter of 64, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

____________, _____________

Answer 1

@vocaloid

Answer 2

What math class is this?

Answer 3

Algebra, this is Quadratic Functions

Answer 4

Intermediate Algebra

Answer 5

Okay, just making sure it isn't calculus. So since this is not calculus you do guess and check to find the dimensions with the largest area. You will find a square to have a larger area than say, a rectangle of the same perimeter. It would be pretty cool if you try this for yourself as well. Plug in 16 and 16 for length and width, 20 and 12 for length and width (respectively), a few more length and widths that have a total Perimeter of 64, and see which has the greatest Area.

Remember: A = L* W
P = 2(L+W)

Answer 6

P = 2(16+12)

Answer 7

?

Answer 8

Plug these in for L and W respectively

(16, 16)
(12, 20)
(2, 30)
(15, 17)

into the area formula, I have already checked and the perimeter for each of these is 64. See which of these had the greatest Area

Answer 9

like this:

A = L* W

A = 16 * 16

?

Answer 10

yes, now 16 times 16 is....?

Answer 11

256

Answer 12

yes, now do the same for the other coordinates

Answer 13

12 * 20 = 240
2 * 30 = 60
15 *17 = 255

Answer 14

good job, so you found that 16*16 gives the largest area

Answer 15

So your answer, or the largest rectangles dimensions, are (16, 16)
write 16 over both or the underlines in the question

Answer 16

i could only do it like this

Answer 17

?

Answer 18

Yes, you can submit

Answer 19

ok

Answer 20

could you answer more for me

Answer 21

Make a new post,