For a right-angled triangle having the lengths of two sides as $2 \sqrt{2}$ and $5$,find the possible lengths of the third side.

If the sum of the distances of a point from two perpendicular lines in a plane is $1$,then its locus is

For what value of $y$ does the triangle with vertices $A(2, 7)$,$B(4, y)$,and $C(-2, 6)$ form a right angle at $A$?

The area of the triangle enclosed by the straight lines $x = 0$,$y = 0$ and $x + 2y + 3 = 0$ in sq. units is:

The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4x + y = 14$ and $3x - 2y = 5$,respectively. The point $\left(2, -\frac{4}{3}\right)$ divides the third side $BC$ internally in the ratio $2:1$. The equation of the side $BC$ is:

The incenter of an equilateral triangle is $(-6, 5)$ and one of its sides lies on the $y$-axis. Find the length of the side of the triangle.