Question

Mr.eldeb is designing a voting box for prom. The box must have a maximum surface area of 380 in2 with a height of 4.5 inches. If the box has a square base what is the largest width that the box could have in inches?

PLEASE HELLPP

Answer 1

Check the picture below.

now, we know the base is a square, thus the length = width, namely L = w, so

`\bf SA=2(Lw+Lh+wh)\implies \stackrel{\textit{since we know that L=w}}{380=2(ww+wh+wh)} \\\\\\ \cfrac{380}{2}=w^2+2wh\implies 190=w^2+2wh \implies 0=w^2+2wh-190 \\\\\\ 0=(w+19)(w-10)\implies w= \begin{cases} -19\\ \boxed{10} \end{cases}`

since the units must be positive, we can't use -19.