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Question Number 206430 by cortano21 last updated on 14/Apr/24

Answered by mr W last updated on 14/Apr/24

$$AB=a,say$$$$7^2=a^2+8^2-2\times 8a\cos 60°$$$$a^2-8a+15=0$$$$(a-3)(a-5)=0$$$$a=5or3(rejected,sinceAD=2amust⩾8)$$$$GD=2a-8=2\times 5-8=2$$$$\frac{DH}{a}=\frac{GD}{8}=\frac{2}{8}=\frac{1}{4}$$$$\Rightarrow DH=\frac{a}{4}\Rightarrow x=\frac{3}{4}a=\frac{15}{4}✓$$

Answered by A5T last updated on 14/Apr/24

$$AD=2a\Rightarrow DG=2a-8$$$$\frac{7}{GH}=\frac{8}{DG}\Rightarrow GH=\frac{7(a-4)}{4}$$$$\frac{a}{DH}=\frac{7}{GH}\Rightarrow DH=\frac{a(a-4)}{4}\Rightarrow x=\frac{8a-a^2}{4}$$$$a^2+8^2-a\times 8=49\Rightarrow 8a-a^2=15\Rightarrow x=\frac{15}{4}$$

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