R. D. Sharma Solutions for Chapter: Quadrilaterals, Exercise 4: EXERCISE

In a $△ABC, D,E$ and $F$ are, respectively, the mid-points of $BC, CA$ and $AB$. If the lengths of side $AB, BC$ and $CA$ are $7 \mathrm{cm}, 8 \mathrm{cm}$ and $9 \mathrm{cm},$ respectively, find the perimeter of $△DEF$.

In a triangle, $P,Q$ and $R$ are the midpoints of sides $BC, CA$ and $AB$ respectively. If $AC=21 \mathrm{cm}, BC=29 \mathrm{cm}$ and $AB=30 \mathrm{cm},$ If the perimeter of the quadrilateral $ARPQ$ is $k \mathrm{cm}$, find the value of $k$.

In the figure, triangle $ABC$ is right-angled at $B.$ Given that $AB=9 \mathrm{cm}, AC=15 \mathrm{cm}$ and $D,E$ are the midpoints of the sides $AB$ and $AC$ respectively. If the length of $BC=x \mathrm{cm}$, then find the value of $x$.

In figure, triangle $ABC$ is right-angled at $B.$ Given that $AB=9 \mathrm{cm},AC=15 \mathrm{cm}$ and $D, E$ are the midpoints of the sides $AB$ and $AC$ respectively, calculate the area of $△ADE$ (in ${\mathrm{cm}}^2$).

The triangle formed by joining the mid-points of the sides of an isosceles triangle is a/an _____ triangle.

The triangle formed by joining the mid-points of the sides of a right triangle is _____.

The figure formed by joining the midpoints of consecutive sides of a quadrilateral is _____.

$BM$ and $CN$ are perpendiculars to a line passing through the vertex $A$ of a triangle $ABC .$ If $L$ is the mid-point of $BC,$ prove that $LM=LN$.