Mathematics, 06.09.2019 01:20 faithkristi
The height of a trapezoid can be expressed as x-4, while the bases can be expressed as x+4 and x+9. if the area of the trapezoid is 99cm^2, find the length of the larger base?
Answers: 1
![\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{bases}{parallel~sides}\\ \cline{1-1} h= x - 4\\ a = x+4\\ b=x+9\\ A=99 \end{cases}\implies 99=\cfrac{(x-4)[(x+4)+(x+9)]}{2} \\\\\\ 99=\cfrac{(x-4)[2x+13]}{2}\implies 198=\stackrel{\mathbb{FOIL}}{2x^2+5x-52}\implies 0=2x^2+5x-250](/tpl/images/0224/0447/76d7b.png)
![\bf 0=(2x+25)(x-10)\implies x= \begin{cases} ~~\begin{matrix} -25 \\[-0.6em]\cline{1-1}\\[-5pt]\end{matrix}~~\\ 10 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{larger base}}{x+9}\implies 10+9\implies 19](/tpl/images/0224/0447/60321.png)
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The height of a trapezoid can be expressed as x-4, while the bases can be expressed as x+4 and x+9....
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