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Question Number 177047 by Ar Brandon last updated on 30/Sep/22

Answered by som(math1967) last updated on 30/Sep/22

$$cosD=\frac{7^2+{DC}^2-5^2}{2\times 7DC}=\frac{24+{DC}^2}{14DC}$$$$againcosD=\frac{7^2+{DB}^2-5^2}{2\times 7\times DB}=\frac{24+{DB}^2}{14DB}$$$$\frac{24+{DC}^2}{14DC}=\frac{24+{DB}^2}{14DB}$$$$\Rightarrow 24DB+DB\times {DC}^2=24DC+DC\times {DB}^2$$$$\Rightarrow 24(DB-DC)=DB\times DC(DB-DC)$$$$DB\times DC=24[\because DB\ne DC]$$$$$$

Commented by Ar Brandon last updated on 30/Sep/22

Thank you Sir

Answered by HeferH last updated on 30/Sep/22

$$$$$$Lethbetheheightof△ABC$$$$h^2=25-\frac{{BC}^2}{4}$$$$h^2+{(\frac{BC}{2}+CD)}^2=49$$$${CD}^2+\left(CD\right)\left(BC\right)=24$$$$CD(CD+BC)=24$$$$CD\left(DB\right)=24$$

Commented by Ar Brandon last updated on 30/Sep/22

Thank you Sir

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