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Find the sizes of squares in rectangle?
Find the integer lengths of squares a to n. See graphic:
No 2 squares are of the same size.
gôhpihán, don't make this problem harder than it has to be. This is a rectangle, not a square, that's dissected into squares. a b ≠ b n, and a ≠ n.
a + b ≠ b + n, and a ≠ n.
Stupid Y!A bug! Still dropping those + signs.
If it's of any help, the graphic is scaled pretty accurately. Go measure.
2 Antworten
- gôhpihánLv 7vor 7 JahrenBeste Antwort
EDIT: Ohhhh... I didn't see the title... my bad.. Will fix it!
EDIT2: FIXED!
Answer is
a = 356, b = 492, c = 115, d = 89, e = 152, f = 26, g = 63, h = 141, i = 104, j = 111, k = 127, l = 245, m = 238, n = 365
Method:
Let f = x, g = y, for y > x > 0, where x and y are integers then
d = f + g = x + y
c = d + f = 2x + y
e = d + g = x + 2y
h = c + f = 3x + y
i = c + h - d - g = 4x
a = c + d + e = 4x + 4y
j = a - h - i = -3x + 3y
l = h + i = 7x + y
m = c + h + l - e - j = 14x - 2y
k = m - j = 17x - 5y
n = k + m = 31x - 7y
b = k + n = 48x - 12y
Because a + c + h + l = b + n, we get 63x = 26y, so the smallest positive integer value of (x,y) is (26,63)
- KoshkaLv 5vor 7 Jahren
Whatever.
The alphabetical order is confusing!
Ascribe size 1*1 area to biggest square, so b=1/1, a=2/3, n=4/9, l=8/27, m=64/729, e (or h?) =4096/531441...................
lim (y^2/x^2) as x -> infinity
-----
The fractions are the areas of the squares.
b=1 m^2
a= 0.6666666....m^2
n= 0.4444444....m^2
l=0.29629629... m^2
m=0.087791495...m^2
e (or h)=0.07707346...m^2
.......
Goodbye!
