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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

User Jshree
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1 Answer

1 vote

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.

Mr.eldeb is designing a voting box for prom. The box must have a maximum surface area-example-1
User Mattinbits
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