R. D. Sharma Solutions for Chapter: Triangles, Exercise 6: EXERCISE 7.6

The areas of two similar triangles are $121 {\mathrm{cm}}^2$and $64 {\mathrm{cm}}^2$, respectively. If the median of the first triangle is $12.1 \mathrm{cm}$, and the corresponding median of the other triangle is $x \mathrm{cm}$, then write the value of $x$.

If $△ABC~△DEF$ such that  $AB=5 \mathrm{cm}$, area $\left(△ABC\right)=20 {\mathrm{cm}}^2$, area $\left(△DEF\right)=45 {\mathrm{cm}}^2$ and $DE=x \mathrm{cm}$, then determine the value of $x$ up to one decimal place.

In $\Delta ABC, PQ$ is a line segment intersecting $AB$ at $P$ and $AC$ at $Q$ such that $PQ\left|\right|BC$ and $PQ$ divides $\Delta ABC$ into two parts equal in area. Find $\frac{BP}{AB}.$

If the required ratio is of the form $\frac{\sqrt{a}-1}{\sqrt{a}}$, then what is the value of $a$? 

The areas of two similar triangles $ABC$ and $PQR$ are in the ratio $9:16.$ If $BC=4.5 \mathrm{cm}$, find the length of $QR$. (Write the numeral value as final answer i.e without unit.)

If $D$ is a point on the side $AB$ of $∆ABC$ such that $AD:DB=3:2$ and $E$ is a point on $BC$ such that $DE\Vert AC$. Find the ratio of areas of $\mathit{∆}ABC$ and $\Delta BDE$.

If the ratio is of the form $p:q$, what is the value of $q$?

If $\Delta ABC$ and $\Delta BDE$ are equilateral triangles, where $D$ is the mid point of $BC$, find the ratio of areas of $\Delta ABC$ and $\Delta BDE$.

If the ratio is of the form $p:q$, what is the value of $p$?

Two isosceles triangles have equal vertical angles and their areas are in the ratio $36:25$. Find the ratio of their corresponding heights.

If the ratio is of the form $p:q$, what is the value of $q$?

In $∆ABC$, $\mathrm{P}$ divides the side $AB$ such that $AP : PB = 1 : 2. Q$ is a point in $AC$ such that $PQ \left|\right| BC$. Find the ratio of the areas of $∆APQ$ and trapezium $BPQC$.