Question

The volume of square pyramid is 141 2/3 cubic inches. The height of the pyramid is two more than three times the lenght of its base . What is the lenght of the base?

Answer 1

`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=base=length* width\\\\ h=height\\ ----------\\ \textit{for a square pyramid}\\ \textit{the base is a square}\\ \textit{thus length=width=x}\\ B=x\cdot x=x^2\\ ----------\\ V=141(2)/(3)\\\\ h=3x+2 \end{cases}`


`\bf V=\cfrac{1}{3}Bh\implies 141(2)/(3)=x^2(3x+2) \\\\\\ \cfrac{425}{3}=3x^3+2x^2\implies 425=9x^3+6x^2\implies 0=9x^3+6x^2-425`

solve for "x"

hmm I tried factoring it, tried a few combos, no dice, haven't graphed it

but, it doesn't seem it factor that neatly, so the solutions are likely decimals with long floats