R. D. Sharma Solutions for Chapter: Triangles, Exercise 10: MULTIPLE CHOICE QUESTIONS (MCQs)

In a $△\mathrm{ABC}$, point $\mathrm{D}$ is on side $\mathrm{AB}$ and point $\mathrm{E}$ is on side $\mathrm{AC}$, such that $\mathrm{BCED}$ is a trapezium. If $\mathrm{DE}:\mathrm{BC}=3:5$, then $\mathrm{Area}\left(△\mathrm{ADE} \right):\mathrm{Area}\left(\square \mathrm{BCED}\right)=$

If $\mathrm{ABC}$ is an isosceles triangle and $\mathrm{D}$ is a point of $\mathrm{BC}$ such that $\mathrm{AD}\perp \mathrm{BC}$, then

$∆\mathrm{ABC}$ is a right triangle right-angled at $\mathrm{A}$ and $\mathrm{AD}\perp \mathrm{BC}$. Then, $\frac{\mathrm{BD}}{\mathrm{DC}}=$

If $\mathrm{E}$ is a point on side $\mathrm{CA}$ of an equilateral triangle $\mathrm{ABC}$ such that $\mathrm{BE}\perp \mathrm{CA}$, then ${\mathrm{AB}}^2+{\mathrm{BC}}^2+{\mathrm{CA}}^2=$

In a right triangle $\mathrm{ABC}$ right-angled at $\mathrm{B}$, if $\mathrm{P}$ and $\mathrm{Q}$ are points on the sides $\mathrm{AB}$ and $\mathrm{AC}$ respectively, then

If $∆\mathrm{ABC}~∆\mathrm{DEF}$ such that $\mathrm{DE}=3 \mathrm{cm}, \mathrm{EF}=2 \mathrm{cm}, \mathrm{DF}=2.5 \mathrm{cm}, \mathrm{BC}=4 \mathrm{cm},$ then perimeter of $∆\mathrm{ABC}$ is

If $∆\mathrm{ABC}~∆\mathrm{DEF}$ such that $\mathrm{AB}=9.1 \mathrm{cm}\text{ and }\mathrm{DE}=6.5 \mathrm{cm}$. If the perimeter of $∆\mathrm{DEF}\text{ is }25 \mathrm{cm}$, then the perimeter of $∆\mathrm{ABC}$ is

In an isosceles triangle $\mathrm{ABC}$ if $\mathrm{AC}=\mathrm{BC}$ and ${\mathrm{AB}}^2=2{\mathrm{AC}}^2$, then $\angle \mathrm{C}=$