ok heres the problem. Irene Drew a rectangle with an area of 196 square units. She finds that this is the largest area possible for any rectangle with the same perimeter. What are the deminsions of the rectangle? What is the perimeter of the rectangle? Explain and justify your method using words, diagrams, or expressions.
ok.
so.i also need to know what type of quadrilateril she drew.
Those who have websites or somehting to show me the picture word s or expressions (without downloading) please show links
Thank You!!!!!!
2007-04-26 15:26:54 · 7 answers · asked by Tristan L 1 in Science & Mathematics ➔ Mathematics
Im not going to look at the awnsers till im done with MY WORK then i will use your awnser to check...thank you very much!
2007-04-26 15:27:36 · update #1
Thank you! all of these awnser helped thanks!
2007-04-26 16:02:46 · update #2
The rectangle that encloses the largest area for a given perimeter is a square, so this is a 14×14 square, and its perimeter is 56 units.
2007-04-26 15:30:52 · answer #1 · answered by Pascal 7 · 0⤊ 1⤋
i could do this, its calculus. Im a sophomore in Honors Calc right now. We just learned this. Its fairly easy. But i hate calc. Actually i will do it so here goes. It is a 14 by 14 square. You use two formulas. one for area and one for perimeter. the formula for area would be: xy=196; one side being x and the other being y. The perimeter formula is 2x + 2y = P; P being perimeter. Solve for y in the area formula. you get 196/x = y. plug 196/x into the perimeter formula wherever there is a y. The new perimeter formula is: 2x + (2(196)) / x = P. Take the derivative of that and you get: 2 - (392 / x^2). X^2 is x squared. solve this equation for x. you come up with 2x^2 = 392. x^2 = 196. x=14. Use the first derivative test to find that this comes to be a maximum.The perimeter of the rectangle would be 56 units. I hope you know calculus because if you dont i just confused the crap out of you. Hope i helped.
2007-04-26 15:45:46 · answer #2 · answered by $p-i-m-p$ 2 · 0⤊ 0⤋
The quadrilateral that maximizes area is the square. So Irene drew a square. Since we know that all sides of a square are equal and that the area is s^2, we can solve:
s^2=196
s=14
The perimeter is 14+14+14+14 or 4*14=56 units
Hope this helps!
2007-04-26 15:35:00 · answer #3 · answered by Anonymous · 0⤊ 1⤋
a square maximizes area. So I believe she drew a 14 x 14 square. So, perimeter would be 56. Reason a square is the largest area is because you are multiplying two large numbers instead of a large number and a small number. If we took a rectangle that was 1by 27, it would have a perimeter of 56, but area would only be 27.
2007-04-26 15:32:18 · answer #4 · answered by leo 6 · 1⤊ 1⤋
Is it 14x14?
The circle has the largest interior for it's perimeter. A squre is closer to this than another shape.
You can try an experiment to test it. use 7X28, perimeter is
2(7+28)=70
2(14+14)=56
2007-04-26 15:34:31 · answer #5 · answered by Ron H 6 · 0⤊ 1⤋
its a square because squares have the largest area with a restricted perimeter. i forgot the conventional proof but i can prove it with calculus if you wants to see it email me.
each of the sides are 14.
2007-04-26 15:33:57 · answer #6 · answered by Miasmarizing 3 · 0⤊ 1⤋
it has to be a 14x14 square because a square will have the most area than any rectangle.
2007-04-26 15:32:33 · answer #7 · answered by Anonymous · 0⤊ 1⤋