Surds

hollydolly98:

if the area of x is 1m squared

a*b=1

hollydolly98:

the ratio of the long side to the short side is root 2

a/b = sqrt(2)

[input]solve( a*b=1, a/b = sqrt(2))[/input]

Area, x = a*b; x = 1
Therefore 1 = a*b_________________ Eq .1

Ratio of sides a and b, a/b, is √2,
Therefore a/b = √2
Hence a = (√2)*b__________________Eq. 2

Eq.2 in Eq.1:
1 = [(√2)*b]*b
1 = (√2)*bsqared
bsquared = 1/√2
b = √(1/√2)

Replace value of b into Eq. 2
Therefore a = (√2)* √(1/√2)

Hence value a = (√2)* √(1/√2) and b = √(1/√2). (Surd format )