Question

The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.

Answer 1

The sides of a square are

5x − 12y − 65 = 0 ... (1)

5x − 12y + 26 = 0 ... (2)

We observe that lines (1) and (2) are parallel. So, the distance between them will give the length of the side of the square.

Let d be the distance between the given lines.

$\Rightarrow d=\left|\frac{-65-26}{\sqrt{5^2+{\left(-12\right)}^2}}\right|=\frac{91}{13}=7$

∴ Area of the square = 7²
= 49 square units