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Question Number 189808 by normans last updated on 22/Mar/23

Answered by mr W last updated on 22/Mar/23

Commented by mr W last updated on 22/Mar/23

$$7^2+{(7+x)}^2={\left(\sqrt{13}a\right)}^2$$$$\Rightarrow x=\sqrt{13a^2-49}-7$$$$$$$$\sqrt{{\left(2a\right)}^2-x^2}+\frac{3a\times x}{2a}=7+x$$$$5x^2-28x+196-16a^2=0$$$$\Rightarrow x=\frac{14-4\sqrt{5a^2-49}}{5}$$$$\frac{14-4\sqrt{5a^2-49}}{5}=\sqrt{13a^2-49}-7$$$$49-4\sqrt{5a^2-49}=5\sqrt{13a^2-49}$$$$58-5a^2=8\sqrt{5a^2-49}$$$$a^4-36a^2+260=0$$$$\Rightarrow a^2=10$$$$bluearea=6a^2=60✓$$

Answered by HeferH last updated on 22/Mar/23

Commented by HeferH last updated on 22/Mar/23

$$7+\frac{2\mathrm{k}}{3}=3\mathrm{k}$$$$\mathrm{k}=3$$$${\mathrm{k}}^2+{9\mathrm{k}}^2={9\mathrm{a}}^2$$$${\mathrm{a}}^2=\frac{{10\mathrm{k}}^2}{9}=10$$$$2\mathrm{a}\times 3\mathrm{a}={6\mathrm{a}}^2={60\mathrm{u}}^2$$

Commented by manxsol last updated on 22/Mar/23

$$$$$$$$$$\mathrm{I}\mathrm{liked}\mathrm{your}\mathrm{solution}.$$$$\mathrm{proportio}n:\left(\mathrm{AB}90\mathrm{AB}\right):\mathrm{tg}.$$

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