Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 206232 by mr W last updated on 09/Apr/24

Answered by A5T last updated on 09/Apr/24

$$S_2=S_1+S_3-2AB\times BCcos\left(\theta \right)$$$$S_1=S_2+S_3-2BC\times ACcos\left(\beta \right)$$$$S_3=S_2+S_1+2AB\times ACcos(\theta +\beta )$$$$S_4=S_1+S_2-2AB\times ACcos(\theta +\beta )$$$$S_5=S_3+S_2+2AC\times BCcos\beta$$$$S_6=S_1+S_3+2AB\times BCcos\theta$$$$\Rightarrow S_1+S_2+...+S_6=4(S_1+S_2+S_3)$$$$\Rightarrow S_4+S_5+S_6=3(S_1+S_2+S_3)=30$$

Commented by mr W last updated on 09/Apr/24

$$great!$$

Answered by mr W last updated on 09/Apr/24

$$if{S}_1+S_2+S_3=10,find{S}_4+S_5+S_6=?$$

Answered by mr W last updated on 10/Apr/24

Commented by mr W last updated on 10/Apr/24

$$f^2=a^2+b^2-2ab\cos (180°-\gamma )=a^2+b^2+2ab\cos \gamma$$$$c^2=a^2+b^2-2ab\cos \gamma$$$$f^2+c^2=2(a^2+b^2)$$$$similarly$$$$e^2+b^2=2(c^2+a^2)$$$$d^2+a^2=2(b^2+c^2)$$$$\Rightarrow d^2+e^2+f^2+a^2+b^2+c^2=4(a^2+b^2+c^2)$$$$\Rightarrow d^2+e^2+f^2=3(a^2+b^2+c^2)$$$$\Rightarrow S_4+S_5+S_6=3(S_1+S_2+S_3)=30$$

Answered by TonyCWX08 last updated on 11/Apr/24

$$\frac{S_4+S_5+S_6}{S_1+S_2+S_3}=3$$$$\frac{S_4+S_5+S_6}{10}=3$$$$S_4+S_5+S_6=30$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com