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Question Number 18461 by b.e.h.i.8.3.417@gmail.com last updated on 22/Jul/17

Answered by mrW1 last updated on 22/Jul/17

$$1)$$$${\mathrm{\Delta }}_{{\mathrm{AA}}_{5\mathrm{B}}{\mathrm{A}}_{60\mathrm{C}}}=\frac{5}{\mathrm{n}}\times \frac{60}{\mathrm{n}}\times {\mathrm{\Delta }}_{\mathrm{ABC}}$$$${\mathrm{\Delta }}_{{\mathrm{BCC}}_{5\mathrm{A}}}=\frac{5}{\mathrm{n}}\times {\mathrm{\Delta }}_{\mathrm{ABC}}$$$$\Rightarrow \frac{300}{{\mathrm{n}}^2}=\frac{5}{\mathrm{n}}$$$$\Rightarrow \mathrm{n}=60$$$$2)$$$${\mathrm{A}}_{5\mathrm{C}}{\mathrm{A}}_{45\mathrm{B}}//\mathrm{BC}\Rightarrow \mathrm{not}\mathrm{possible}$$$${\mathrm{C}}_{90\mathrm{A}}{\mathrm{C}}_{10\mathrm{B}}\mathrm{\perp }\mathrm{BC}$$

Commented by b.e.h.i.8.3.417@gmail.com last updated on 22/Jul/17

$$thankyouverymuchdearmrW1.$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$$$

Commented by mrW1 last updated on 22/Jul/17

Commented by mrW1 last updated on 23/Jul/17

$${\mathrm{C}}_{10\mathrm{A}}{\mathrm{C}}_{90\mathrm{B}}\mathrm{\perp }\mathrm{BC}$$$$\Rightarrow \frac{90}{10}=\frac{\mathrm{CX}}{\mathrm{CA}}=\frac{\mathrm{x}}{\mathrm{b}}$$$$\mathrm{x}=\mathrm{b}\cos \mathrm{C}=\mathrm{b}\frac{{\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2}{2\mathrm{ab}}=\frac{{\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2}{2\mathrm{a}}$$$$\Rightarrow \frac{90}{10}=\frac{{\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2}{2\mathrm{ab}}$$

Commented by mrW1 last updated on 23/Jul/17

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