Question

The equation of two sides of a square whose area is $25$ square units are $3x-4y=0$ and $4x+3y=0$. The equations of the other two sides of the square are

• A. $3x-4y\pm 25=0,4x+3y\pm 25=0$
• B. $3x-4y\pm 5=0,4x+3y\pm 5=0$
• C. $3x-4y\pm 5=0,4x+3y\pm 25=0$
• D. None of these

Answer 1

The correct option is A $3x-4y\pm 25=0,4x+3y\pm 25=0$

Area of square $=25$

The equation of 2 sides are $3x-4y=0$ and $4x+3y=0$

$\therefore a^2=25$

$\Rightarrow a=5$ units.

Since it is a square, opposite sides are parallel. Parallel lines have same equation but for constant.

Hence the other two sides of the square are :

$\Rightarrow 3x-4y+m=0$ and $4x+3y+n=0$

Distance between $3x-4y=0$ $3x-4y+m=0$ is $5$ unit \dfrac{m-0}{5}=5$

$\Rightarrow m=\pm 25$

$\therefore ax+by+c_1=0$ $\xi$ $ax+by+c_2=0$

$\Rightarrow \frac{c_1-c_2}{\sqrt{a_1^2+b^2}}$

$\therefore 3x-4y\pm 25=0$ and $4x+3y\pm =0$

Hence, the answer is $3x-4y\pm 25=0$ and $4x+3y\pm 25=0.$