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Question Number 189743 by normans last updated on 21/Mar/23

Answered by mr W last updated on 21/Mar/23

Commented by mr W last updated on 21/Mar/23

$${\left(2h\right)}^2=4a\times a$$$$\Rightarrow h=a$$$$h_1=\frac{5a}{2}$$$$\frac{h_2}{2h}=\frac{5a-h_2}{4a}$$$$\Rightarrow h_2=\frac{5a}{3}$$$$A_3=\frac{5{ah}_2}{2}=\frac{5a}{2}\times \frac{5a}{3}=\frac{25a^2}{6}$$$$A_1+A_3=\frac{5{ah}_1}{2}=\frac{5a\times 5a}{2\times 2}=\frac{25a^2}{4}$$$$\Rightarrow A_1=\frac{25a^2}{4}-\frac{25a^2}{6}=\frac{25a^2}{12}$$$$A_2+A_3=\frac{5a\left(2h\right)}{2}=5a^2$$$$\Rightarrow A_2=5a^2-\frac{25a^2}{6}=\frac{5a^2}{6}$$$$\Rightarrow \frac{A_1}{A_2}=\frac{25}{12}\times \frac{6}{5}=\frac{5}{2}✓$$

Answered by HeferH last updated on 21/Mar/23

$${\left(2\mathrm{x}\right)}^2={\left(2\mathrm{a}\right)}^2$$$$\mathrm{a}=\mathrm{x}$$$$\frac{\mathrm{Green}}{\mathrm{Blue}}={\left(\frac{\frac{5\mathrm{a}}{2}\sqrt{2}}{\mathrm{a}\sqrt{5}}\right)}^2={(\frac{5}{2}\sqrt{2}\cdot \frac{1}{\sqrt{5}})}^2=\frac{25\cdot 2}{4\cdot 5}=\frac{5}{2}$$$$$$

Commented by HeferH last updated on 21/Mar/23

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