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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.

Feb 10, 2021

#1
+11656
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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.

Hello Guest!

$$6x-8y+5=0\\ f(x)=\frac{3}{4}x+0.625\\ 3x-4y+10=0\\ g(x)=\frac{3}{4}x+2.5$$

$$y=mx+n\\ m_{f,g}=0.75$$

$$\alpha =arctan(m)$$

$$A=a^2\\ a= (g(0)-f(0))\cdot cos(\alpha)\\ a =(g(0)-f(0))\cdot cos(arctan(m))\\ a =(2.5-0.625)\cdot cos(arctan(0.75))=\color{blue}1.5$$

$$A=[(2.5-0.625)\cdot cos(arctan(0.75))]^2$$

$$A=2.25$$

!

Feb 10, 2021