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.
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
