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Question Number 174664 by dragan91 last updated on 07/Aug/22

Answered by mr W last updated on 07/Aug/22

$$\frac{b-5}{5}=\frac{5}{a-5}$$$$\Rightarrow ab=5(a+b)$$$$letu=a+b,v=ab$$$$\Rightarrow v=5u$$$$$$$$\frac{a(1-\frac{\sqrt{24}}{\sqrt{a^2+b^2}})}{\sqrt{24}}=\frac{\sqrt{24}}{\frac{b\sqrt{24}}{\sqrt{a^2+b^2}}}$$$$ab(\frac{\sqrt{{(a+b)}^2-2ab}}{\sqrt{24}}-1)={(a+b)}^2-2ab$$$$u^2-10u-600=0$$$$(u+20)(u-30)=0$$$$\Rightarrow u=30,v=150$$$$A_{yellow}=ab-24-25=150-24-25=101✓$$

Commented by Tawa11 last updated on 08/Aug/22

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

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