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Question Number 215454 by cherokeesay last updated on 07/Jan/25

Answered by mr W last updated on 07/Jan/25

Commented by mr W last updated on 15/Jan/25

$$EB=2a$$$$EA=2b$$$$CB=\sqrt{3}a$$$$DA=\sqrt{3}b$$$$\frac{1}{2}\times (2b-a)\sqrt{3}a=2\times 8$$$$\frac{1}{2}\times (2a-b)\sqrt{3}b=2\times 15$$$$\frac{(2a-b)b}{(2b-a)a}=\frac{15}{8}$$$$15a^2-14ab-8b^2=0$$$$(3a-4b)(5a+2b)=0$$$$\Rightarrow \frac{a}{b}=\frac{4}{3}$$$$\frac{1}{2}\times (2\times \frac{4b}{3}-b)\sqrt{3}b=2\times 15$$$$\sqrt{3}{b}^2=36$$$$\Rightarrow b=\frac{6}{\sqrt{\sqrt{3}}}\Rightarrow a=\frac{8}{\sqrt{\sqrt{3}}}$$$$\mathrm{\Delta }ABE=\frac{2a\times 2b\sin 60°}{2}=\sqrt{3}ab=48$$$$?=48-8-15=25✓$$

Commented by mr W last updated on 07/Jan/25

Commented by cherokeesay last updated on 07/Jan/25

$$sonice!$$$$thankyousomuchmaster!$$

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