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Two sides of a square are consecutively based upon two straight lines 5x - 8y + 5 = 0 and 3x - 4y + 10 = 0.  Find the area of this square.

 Jan 2, 2020
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Straight line 1 is:

5x-8y+5=0 

well solve for y 

-8y=-5x-5

8y=5x+5 

divide by 8

\(y=\frac{5}{8}x+\frac{5}{8}\)

Straight line 2 is:

3x-4y+10=0

4y=3x+10 

divide by 4

\(y=\frac{3}{4}x+\frac{10}{4}\)

Well 2 sides of square are based upon two straight lines, so both sides of square must be equal (Actually 4 sides of square are equal but let's see the context here) , so the 2 equations must be equal I.e.

\(\frac{5}{8}x+\frac{5}{8}\)=\(\frac{3}{4}x+\frac{10}{4}\)

solve for x 

x=-15   (I.e. the length of square can't be negative but this square is in a negative quadrant that's why the x value is -15 but we write it just as 15)

So, area of square = s^2 , (-15)^2=225

 Jan 3, 2020

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