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$(x-4.5)(x+4.5) = 135$ and also $x^2 = 135$.

You have actually to collection up two equations. We recognize that the basic $x$ is $4.50 ext cm$ much shorter then the height $y$. Hence,

$$y=x+4.50 ext cm.$$

The surface ar area $A$ is provided by

$$A=xy=135 ext cm^2.$$

Plugging $y=x+4.50 ext cm$ into the equation for the surface area we obtain:

$$135 ext cm^2=x(x+4.50 ext cm) implies x^2+4.5x-135 =0.$$

Now, settle with the quadratic formula to obtain $x$ in $ extcm$. Deserve to you perform this?

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