Two sides of a square are consecutively based upon two straight lines $6\times x - 8\times y + 5 = 0$ and $3\times x - 4 \times y + 10 = 0$. Find the area of this square.
+15001 Two sides of a square are consecutively based upon two straight lines $6\times x - 8\times y + 5 = 0$ and $3\times x - 4 \times y + 10 = 0$. Find the area of this square.
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\(6x-8y+5=0\\ f(x)=\frac{3}{4}x+0.625\\ 3x-4y+10=0\\ g(x)=\frac{3}{4}x+2.5\)
\(y=mx+n\\ m_{f,g}=0.75\)
\(\alpha =arctan(m)\)
\(A=a^2\\ a= (g(0)-f(0))\cdot cos(\alpha)\\ a =(g(0)-f(0))\cdot cos(arctan(m))\\ a =(2.5-0.625)\cdot cos(arctan(0.75))=\color{blue}1.5\)
\(A=[(2.5-0.625)\cdot cos(arctan(0.75))]^2\)
\(A=2.25\)
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