Question

If two opposite sides of a square lie on the lines 3x + 4y = 7 and 3x + 4y + 3 = 0. What is the area of the square in (sq.unit)?

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Answer 1

Slope of line $3x+4y=7$ is $\frac{-3}{4}$ and slope of line $3x+4y+3=0$ is $\frac{-3}{4}$
Slope of line 3x+4y =7 is equal to slope of $3x+4y+3=0$
3x+4y=7 and 3x+4y+3=0 are the parallel lines.
We know that length of side of the square is equal to distance between parallel lines.
Distance between parallel line=
$=|\frac{c_1-c_2}{\sqrt{a^2+b^2}}|$ where lines are $ax+by+c_1=0andax+by+c_2=0$
Lines 3x+4y-7=0 $\&$ 3x+4y+3=0
Side of square =$|\frac{-7-(-3)}{\sqrt{3^2+4^2}}|=|\frac{10}{5}|=2$
Area of the square =$(2{)}^2=4$ sq. unit