Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Quadrilaterals, Exercise 5: Challengers*

If $PQRS$ is a trapezium such that $PQ=30 \mathrm{cm}$ and $PS=18 \mathrm{cm}$ and $L, M$ are the mid-points of the diagonals $PR$ and $QS$ respectively, then length of $LM$ is equal to

$ABCD$ is a square. If $P,Q, R$ and $S$ are points on the sides $AB, BC, CD$ and $DA$ respectively, such that $AP=BQ=CR=DS$, then the value of $\angle SPQ$ is equal to

$ABCD$ is a quadrilateral such that $BC=BA$ and $CD>AD$ Which one of the following is correct?

Two light rods $AB=a+b$ and $CD=a-b$ symmetrically lying on a horizontal. These are kept intact by two strings $AC$ and $BD$. The perpendicular distance between rods is a. The length of $AC$ is given by

$ABCD$ is a parallelogram. The diagonals $AC$ and $BD$ intersect at a point $O$. If $E, F, G$ and $H$ are the mid-psints of $AO, DO, CO$ and $BO$ respectively. Then the ratio of $\frac{\left(EF+FG+GH+HE\right)}{\left(AD+DC+CB+BA\right)}$ is equal to

If a triangle and a convex quadrilateral are drawn cn the same base and no part of the quadrilateral is outside the triangle. Then what will be the relation between the perimeter of the triangle and the perimeter of the quadrilateral.

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a units. The distance between their feet being equal to $b$ units. Then, the area of the thombus is

Constructed externally on the sides $AB, AC$ of $△ABC$ are equilateral triangle $ABX$ and $ACY$. If $P, Q, R$ are the mid-ponts of $AX, AY$ and $BC$ respectively, then $△PQR$ is