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Question Number 206321 by cortano21 last updated on 12/Apr/24

Answered by TonyCWX08 last updated on 12/Apr/24

$$By\mathrm{\Delta }BCD\backsim \mathrm{\Delta }CDE$$$$\frac{x}{\sqrt{14}}=\frac{7\sqrt{14}}{x}$$$$x^2=98$$$$$$$$UsingPythagorasTheoremin\mathrm{\Delta }ABD$$$$x^2+{\left(7\sqrt{14}\right)}^2={AB}^2$$$$98+686={AB}^2$$$${AB}^2=784$$$$AB=28$$

Answered by mr W last updated on 12/Apr/24

Commented by mr W last updated on 12/Apr/24

$$DC=AD$$$$\frac{DE}{DC}=\frac{DE}{AD}=\frac{AD}{DB}$$$$\Rightarrow {AD}^2=DE\times DB=\sqrt{14}\times 7\sqrt{14}=7\times 14$$$$AB=\sqrt{7\times 14+{\left(7\sqrt{14}\right)}^2}=28$$

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