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?

In a $\triangle ABC$,$D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE \parallel BC$. Suppose $BE$ and $CD$ intersect at $O$. If the areas of $\triangle ADE$ and $\triangle ODE$ are $3$ and $1$ respectively,find the area of $\triangle ABC$.

The incentre of the triangle formed by the lines $x = 0$,$y = 0$,and $3x + 4y = 12$ is

The equations of the sides $AB$,$BC$,and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 15a$,and $x - y = 3$ respectively. If its orthocentre is $(2, a)$,where $-\frac{1}{2} < a < 2$,then $p$ is equal to...

The equation of a straight line,perpendicular to $3x - 4y = 6$ and forming a triangle of area $6 \text{ sq. units}$ with the coordinate axes,is

Consider a $\triangle ABC$ in the $XY$-plane with vertices $A=(0,0)$,$B=(1,1)$,and $C=(9,1)$. If the line $x=a$ divides the triangle into two parts of equal area,then $a$ equals