Surds

[hollydolly98 offline]

if the area of x is 1m squared and the ratio of the long side to the short side is root 2, calculate the measurements of the length and width leaving the answer in surd form if possible... please help i have no idea how to do this,

[admin]

if the area of x is 1m squared

a*b=1

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

a/b = sqrt(2)

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

[Gast offline]

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 )