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Question Number 206093 by mr W last updated on 06/Apr/24

Answered by A5T last updated on 07/Apr/24

Commented by A5T last updated on 07/Apr/24

$$S_4+S_1+S_5+S_2+S_6+S_3=S+S_7+S_8...\left(i\right)$$$$S_4+S_7+S_3+S_1+S_8+S_2=S+S_5+S_6...\left(ii\right)$$$$\left(i\right)-\left(ii\right):S_5+S_6-S_7-S_8=S_7+S_8-S_5-S_6$$$$\Rightarrow S_5+S_6=S_7+S_{8}into\left(i\right)$$$$\Rightarrow S_4+S_1+S_2+S_3=S$$

Commented by mr W last updated on 07/Apr/24

$$yessir!thanks!$$

Answered by mr W last updated on 07/Apr/24

Commented by mr W last updated on 07/Apr/24

$$\mathrm{\Delta }BCG=\mathrm{\Delta }BGD$$$$\mathrm{\Delta }DAE=\mathrm{\Delta }DEB$$$$\mathrm{\Delta }BCG+\mathrm{\Delta }DAE=\mathrm{\Delta }BGD+\mathrm{\Delta }DEB$$$$\Rightarrow S_1+S_5+S_2+S_3+S_7+S_4=S_6+S+S_8...\left(i\right)$$$$similarly$$$$S_1+S_8+S_4+S_2+S_6+S_3=S_5+S+S_7...\left(ii\right)$$$$\left(i\right)+\left(ii\right):$$$$2(S_1+S_2+S_3+S_4)=2S$$$$\Rightarrow S=S_1+S_2+S_3+S_4✓$$

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