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Question Number 61825 by Tawa1 last updated on 09/Jun/19

Answered by mr W last updated on 10/Jun/19

Commented by mr W last updated on 10/Jun/19

$$\frac{q}{4}=\frac{p}{7}$$$$\Rightarrow q=\frac{4p}{7}$$$$\frac{4+p}{a}=\frac{7+q}{9}$$$$\Rightarrow 9(4+p)=a(7+q)$$$$\Rightarrow 36+9p=7a+\frac{4ap}{7}$$$$\Rightarrow p=\frac{49a-252}{63-4a}$$$$\frac{q\times a}{4}+\sqrt{7^2-p^2}=9$$$$\Rightarrow \frac{ap}{7}+\sqrt{7^2-p^2}=9$$$$\Rightarrow \frac{a(49a-252)}{7(63-4a)}+\sqrt{49-{\left(\frac{49a-252}{63-4a}\right)}^2}=9$$$$\Rightarrow a\approx 6.9282$$$$A_{green}=\frac{7\times a}{2}\approx 24.25$$

Commented by Tawa1 last updated on 10/Jun/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Commented by MJS last updated on 10/Jun/19

$$\mathrm{the}\mathrm{red}\mathrm{eq}\mathrm{can}\mathrm{be}\mathrm{solved}\mathrm{exactly}$$$$a=\pm 4\sqrt{3}\vee a=\pm 9$$$$4\sqrt{3}\approx 6.9282$$

Commented by mr W last updated on 10/Jun/19

$$thankyousir!$$$$i{didn}^{\prime }tgofurther,sinceitledtoa$$$$quadraticequation.$$

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