Ratio for different paper sizes, using x and y, where x STARTS off as the shorter side and Y STARTS off as the longer side.
A4 = X : Y
A3 = Y : 2X
A2 = 2X : 2Y
A1 = 2Y : 4X
As paper sizes use the same ratio, we say that the ratio for each sizes are equal
Therefore: X:Y = Y:2X = 2X:2Y (simplifies to X:Y) = 2Y:4X (simplifies to Y:2X)
Therefore: X/Y = Y/2X
(Make y the subject)
1) X/Y = Y/2X
2) X = Y²/ 2X
3) 2X² = Y²
4) √(2x²) = Y
5) X√2 = Y
Ratio of A4 is x:y (sub in y= x√2)
X:X√2
Side lengths of Paper
We know the area of A0 is 1m²
The ratio of A0 is 4X:4Y
Therefore the area is:
16XY = 1
XY = 1/16 (sub in y= x√2)
X(x√2) = 1/16
X²√2 = 1/16
X² = 1/16 ÷ √2
X² = (√2)/16
X = √((√2)/32)
X = 0.210m (sub x into y= x√2)
Y= 0.297m
Short (cm) : Long (cm)
A4: 21.0 : 29.7
A3: 29.7 : 42.0
A2: 42.0 : 59.4
A1: 59.4 : 84.0
A0: 84.0 : 118.8