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Question Number 173644 by infinityaction last updated on 15/Jul/22

Answered by mr W last updated on 16/Jul/22

Commented by mr W last updated on 16/Jul/22

$$\frac{8-h_1}{h_1}=\frac{x}{18}$$$$\Rightarrow h_1=\frac{144}{18+x}$$$$\frac{8-h_2}{h_2}=\frac{x}{12}$$$$\Rightarrow h_2=\frac{96}{12+x}$$$$\frac{8-h_3}{h_3}=\frac{x}{6}$$$$\Rightarrow h_3=\frac{48}{6+x}$$$$shadedarea=\frac{1}{2}(18h_1-12h_2-6h_3)$$$$10=\frac{1}{2}(\frac{18\times 144}{18+x}-\frac{12\times 96}{12+x}-\frac{6\times 48}{6+x})$$$$\frac{5}{72}=\frac{9}{18+x}-\frac{4}{12+x}-\frac{1}{6+x}$$$$\frac{5}{72}=\frac{4x^2+36x}{(18+x)(12+x)(6+x)}$$$$(x-6)(5x^2-78x-1080)=0$$$$\Rightarrow x=6✓$$$$\Rightarrow x=\frac{39+3\sqrt{769}}{5}\approx 24.439✓$$

Commented by infinityaction last updated on 16/Jul/22

$$thankssir$$

Commented by Tawa11 last updated on 16/Jul/22

$$\mathrm{Great}\mathrm{sir}$$

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