Mathematics - Area Under Curves Question with Solution | TestHub

The given lines are $4x+3y-20=0$ and $4x+3y+15=0$.

Since the coefficients of $x$ and $y$ are the same, the lines are parallel and represent opposite sides of the square.

The distance between the parallel lines $Ax+By+C_1=0$ and $Ax+By+C_2=0$ is given by $d=\frac{|C_1-C_2|}{\sqrt{A^2+B^2}}$.

Substituting the values, we get:

$d=\frac{|-20-15|}{\sqrt{4^2+3^2}}$

$d=\frac{|-35|}{\sqrt{25}}=\frac{35}{5}=7$

The side of the square is $7$ units.

Area of the square $=(\text{side}{)}^2=7^2=49$ sq. units.

Answer: 49 sq. units