There a perfect SQUARE whose EACH SIDE IS 400 inches. The SQUARE is divided into 7 equal pieces. What is the perimeter of only 2 pieces.....[out of the 7]??
pllleaasseee help!! =]
Thank You
2006-10-05 08:24:33 · 10 answers · asked by ♥ AnGeL ♥ 3 in Science & Mathematics ➔ Mathematics
also......another thing.....the pieces are divided like a pizza pie.......from 1 point in the center.....
2006-10-05 08:35:41 · update #1
1209,486 inches....I may be wrong though.
Additional details: use Autocad...draw a square, divide it and measure the distances...unfortunatelly i don't have it installed for the moment
2006-10-05 08:27:59 · answer #1 · answered by Λиδѓεy™ 6 · 0⤊ 0⤋
We know the area of each piece, 22857.14 sq in. Therefore, the total area is 45714.29 sq in.
Suppose that the square is cut so that the two pieces have the form shown here: http://i105.photobucket.com/albums/m229/jlambers/square27.jpg
Then, the area of these pieces is 40000 sq in (for the triangle whose vertices are the center and two right corners) + the area of the two thin triangles.
The area of each triangle is 2857.14 sq in, and its height is 200. Therefore the length of its base, from the formula A=(1/2)bh, is b=2A/h=28.5714.
We need the leftmost sides of the thin triangles. For that, use the law of cosines. The angle between the side of length 200*sqrt(2) (the line segment between the center and the corner) and the side of length 28.5714 is 45 degrees. Therefore ,the length of the third side is
sqrt((200*sqrt(2))^2 + 28.5714^2 - 2*200*sqrt(2)*28.5714*cos(45)) = 263.42.
Therefore, the total perimeter is 2*263.42 + 2*28.57+400=1492.52 in.
NOTE: regarding the comments in the answer below, there are infinitely many ways to divide up a square into seven pieces of equal area. I'm assuming, based on the problem statement, that the perimeter of any 2 pieces will be the same, so I'm choosing (part of) a partition and working with it. I don't know if this really is the case, but the problem statement doesn't provide any guidance on this issue, so I'm going with this strategy.
2006-10-05 08:54:18 · answer #2 · answered by James L 5 · 0⤊ 0⤋
The perimeter of a square is 4 times the length of a side:
4(400) = 1600
The area of this square 16 sq in
If the Square was cut into 7 equal pieces, the area of each piece's area would be the same:
16/7 = 2.29 sq in
The base of each equal piece would be 1/7 of the perimeter:
1600/7 = 228.57
The area of a triangle is (1/2) bh with b as base and h as the height and the area of each piece is 2.29
the perimeter of each piece is a+b+c
and a^2 + b^2 = c^2
we know that one of the sides of the triangle is 228.57
I'm really sorry Ive been working on this for awhile, I tried different things, but maybe you can use some of the stuff I tried. I dont know how right it is but maybe you'll come up with something from what I did already.
Sorry!
2006-10-05 09:04:33 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I'm assuming it is divided into 7 equal pieces of rectangles.
The the width of each rectangle is 400/7 and the length is 400. The perimeter of each piece is (400/7+400)*2 so the perimeter of both is (400/7+400)*4.
2006-10-05 08:29:09 · answer #4 · answered by thierryinho 2 · 0⤊ 0⤋
I think he's right, but I'm not entirely sure on whether or not you can apply the fact that the height of each triangle is 200 on every one, since the distance from the center to a point on the square is not going to be 200 every time (like in a circle). I think the perimeters of the pieces will be different -- so we need to know _exactly_ which two pieces will be chosen.
2006-10-05 08:54:26 · answer #5 · answered by Jonny Jo 3 · 0⤊ 0⤋
What? that's hard, I have NO idea.
That's a perfect square with 400 inches on each of the four sides,
1600 divided by seven is 228.5 but I can't figure what 2/7 of that is even with a calculator.So I can't help, sorry.
2006-10-05 08:39:55 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Cool!
457.1428571
400 div by 7 = 57
57 x 4 = 1 block
2006-10-05 08:26:16 · answer #7 · answered by god knows and sees else Yahoo 6 · 0⤊ 0⤋
gud question angel but can u tell in which type of equal parts is the given square is divide.
2006-10-05 08:34:02 · answer #8 · answered by Amarbir Singh 2 · 0⤊ 0⤋
I'll be interested in seeing this answer myself! Good luck
2006-10-05 08:28:27 · answer #9 · answered by MollyMAM 6 · 0⤊ 0⤋
914.28571
dont know if thats right, but worth a shot
2006-10-05 08:28:01 · answer #10 · answered by taylorswift<3 3 · 0⤊ 0⤋