In the figure given below,a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles. What is the perimeter of each of the smaller rectangles?

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:

Let a triangle be bounded by the lines $L_{1}: 2x + 5y = 10$,$L_{2}: -4x + 3y = 12$,and the line $L_{3}$,which passes through the point $P(2, 3)$,intersects $L_{2}$ at $A$ and $L_{1}$ at $B$. If the point $P$ divides the line segment $AB$ internally in the ratio $1:3$,then the area of the triangle is equal to

The equations of the sides of a triangle are $x - 3y = 0$,$4x + 3y = 5$,and $3x + y = 0$. The line $3x - 4y = 0$ passes through:

The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is

The length of the altitude through $A$ of the triangle $ABC$,where $A \equiv (-3, 0)$,$B \equiv (4, -1)$,and $C \equiv (5, 2)$,is