The rectangular base is $4.50 \text{ cm}$ shorter than the height and the rectangle has a surface area of $135 \text{ cm}$. Solve the rectangle height with an equation. I know and feel that this is pretty easy, but don't know where I am making a mistake.
So far I have tried
$(x-4.5)(x+4.5) = 135$ and $x^2 = 135$.
Best Answer
You have to set up two equations. We know that the base $x$ is $4.50 \text{ cm}$ shorter then the height $y$. Hence,
$$y=x+4.50 \text{ cm}.$$
The surface area $A$ is given by
$$A=xy=135 \text{ cm}^2.$$
Plugging $y=x+4.50 \text{ cm}$ into the equation for the surface area we obtain:
$$135\text{ cm}^2=x(x+4.50\text{ cm}) \implies x^2+4.5x-135 =0.$$
Now, solve with the quadratic formula to obtain $x$ in $\text{cm}$. Can you do this?