Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
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 Answers
- gôhpihánLv 78 years agoFavorite Answer
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 58 years ago
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!
