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Question Number 208111 by mr W last updated on 05/Jun/24

Commented by mr W last updated on 05/Jun/24

$$yellowarea=?$$

Answered by A5T last updated on 05/Jun/24

Commented by A5T last updated on 05/Jun/24

$$\frac{1}{2}(s+AB)t=14\Rightarrow AB=\frac{28}{t}-s$$$$(t-\frac{16}{s})\times \frac{BC}{2}=2\Rightarrow BC=\frac{4s}{st-16}$$$$(AB+BC)\times \frac{t}{2}=8\Rightarrow AB+BC=\frac{16}{t}$$$$\Rightarrow (\frac{28-st}{t}+\frac{4s}{st-16})=\frac{16}{t}$$$$\Rightarrow 28-st+\frac{4st}{st-16}=16$$$$\Rightarrow {\left(st\right)}^2-32st+192=0\Rightarrow st=8orst=24$$$$\Rightarrow Yellowarea=24-8-6-2=8$$

Commented by mr W last updated on 05/Jun/24

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Answered by mr W last updated on 05/Jun/24

Commented by mr W last updated on 05/Jun/24

$$\frac{2}{8}={\left(\frac{y}{a}\right)}^2\Rightarrow \frac{y}{a}=\frac{1}{2}$$$$\frac{6+2}{6+8}=\frac{x+y}{x+a}\Rightarrow \frac{x+y}{x+a}=\frac{4}{7}\Rightarrow \frac{x}{a}=\frac{1}{6}$$$$\frac{z}{a}=1-\frac{1}{6}-\frac{1}{2}=\frac{1}{3}$$$$\frac{A+2}{6+2}=\frac{z+y}{x+y}=\frac{\frac{1}{3}+\frac{1}{2}}{\frac{1}{6}+\frac{1}{2}}=\frac{5}{4}$$$$\Rightarrow A=\frac{5}{4}\times 8-2=8✓$$

Commented by Tawa11 last updated on 21/Jun/24

$$\mathrm{weldone}\mathrm{sir}$$

Answered by A5T last updated on 05/Jun/24

Commented by A5T last updated on 05/Jun/24

$$(t-\frac{16}{s})\times \frac{BC}{2}=2\Rightarrow BC=\frac{4s}{st-16}$$$$\frac{2}{8}=\frac{{BC}^2}{s^2}\Rightarrow BC=\frac{s}{2}$$$$\Rightarrow \frac{4s}{st-16}=\frac{s}{2}\Rightarrow st=24$$$$\Rightarrow Yellowarea=24-8-6-2=8$$

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