Quadratics: Word Problem (Height, Width)

Question

We're learning about Quadratics, but I'm not exactly sure how this applies to it:

$\dfrac{w + h}{w} = \dfrac{w}{h}$. If the height is 16 inches, what is its width? (Round to the nearest tenth.)

Can someone help me out?

Answer 1

If we substitute $16$ for $h$ in the expression $$\frac{w + h}{w} = \frac{w}{h}$$ we obtain $$\frac{w + 16}{w} = \frac{w}{16}$$ If we multiply both sides of the equation by $16w$ (or cross-multiply), we obtain \begin{align*} 16(w + 16) & = w^2\\ 16w + 256 & = w^2\\ 0 & = w^2 - 16w - 256 \end{align*} which is a quadratic equation in $w$, which you can solve by completing the square of applying the Quadratic Formula.

Answer 2

Plug in $h=16$ and multiply both sides by $16w$ to have $$ 16(w+16)=w^2 $$