## Surds

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### Surds

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,
hollydolly98 offline
Beiträge: 1
Registriert: Fr Mai 11, 2012 8:34 pm

### Re: Surds

hollydolly98 hat geschrieben:if the area of x is 1m squared

a*b=1

hollydolly98 hat geschrieben: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))
Beiträge: 1232
Registriert: Mi Jan 25, 2012 8:27 am

### Re: Surds

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 )
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