Similar triangles

If triangle $ABC$ is similar to triangle $DEF$ such that $BC=3 \mathrm{cm}$, $EF=4 \mathrm{cm}$ and area of triangle $ABC=54 {\mathrm{cm}}^2$, then the area of triangle $DEF$ is:

The triangle $△\mathrm{ABC}$ and $△\mathrm{DEF}$ are similar and the areas are respectively $81 {\mathrm{cm}}^2$ and $196 {\mathrm{cm}}^2$. If $EF = 19.6 \mathrm{cm}$ then find the length of the side $BC$.

In $∆ABC$, $D$ and $E$ point in such that $DE\parallel BC$ and $AD:BD=2:3$, then find the ratio of the area of parallelogram $DECB$ and $∆ABC$:

In Figure, $DEFG$ is a square an $\angle BAC = 90°$. If $BD = 16 \mathrm{cm}$ and $EC = 9 \mathrm{cm}$, then find $DE?$

The $∆ABC$ and $∆DEF$ are similar and their areas be $64 {\mathrm{cm}}^2$ and $121 {\mathrm{cm}}^2$ respectively. If $EF=30.8 \mathrm{cm}$, then $BC$ is:

In the figure $\angle A=\angle CED$, then the find the value of $x$.

In the adjoining figure, $AB, EF$and $CD$ are parallel lines. Given that $EG = 5\mathrm{cm}, GC = 10\mathrm{cm}$ and $DC =18\mathrm{cm}$, then is $EF$ equal to:

In $∆ABC$, $D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE\parallel BC$ and $DE$ divides the $∆ABC$ in to two parts of equal areas. Then ratio of $AD$ and $BD$ is:

The vertical angles of two isosceles triangles are same and the ratio of their areas is $9:16$. Then the ratio of their heights is:

In $∆\mathrm{PQR}$, a line $XY$ is draw parallel to $QR$. If $PQ = 3PX$, then what is the ratio of the area of $∆\mathrm{PXY}$ to the area of $∆\mathrm{PQR}$?

$△\mathrm{ABC}$ is a right angled triangle where $\angle \mathrm{B} = {90}^{º}$ and $\mathrm{BD} \perp \mathrm{AC}$

If,

$$\begin{gathered} \mathrm{BD}=8 \mathrm{cm} \\ \mathrm{AD}=4 \mathrm{cm} \end{gathered}$$

In the figure, $AP = 3 \mathrm{cm} , AR = 4.5 \mathrm{cm} , AQ = 6 \mathrm{cm} , AB = 5 \mathrm{cm}$and $AC = 10 \mathrm{cm}$. Find the length of $AD$ ?
 

The $∆ABC$ and $∆DEF$ are similar and their areas be $64 {\mathrm{cm}}^2$ and $121 {\mathrm{cm}}^2$ respectively. If $EF=15.4 \mathrm{cm}$, then $BC$ is:

In following figure, $∆ABC~∆ADE$. If $AC=5 \mathrm{cm}$, $BC=10 \mathrm{cm}$ and $DE=2 \mathrm{cm}$, then determine $AE$:

A 1.5 m tall boy stands at a distance of 2 m from the lamp post and casts a shadow of 4.5 m on the ground. Find the height of the lamp post?

In $∆ABC, D$ is a point on side $BC$ such that $\angle \mathrm{ADC}=\angle \mathrm{BAC}$. If $CA=12 \mathrm{cm}, CB=8 \mathrm{cm}$ then $CD$ is equal to:

In a $\mathrm{\Delta } \mathrm{ABC}, \mathrm{DE}$ is parallel to $\mathrm{BC}, \mathrm{AD} = 3$ cm, $\mathrm{AE} = 4$ cm and $\mathrm{AC} = 10$ cm, then the value of $\mathrm{BD}$ in centimetres is:

The areas of two similar triangles are $324 {\mathrm{cm}}^2$ and $225 {\mathrm{cm}}^2$. If the altitude of the smaller triangle is $10 \mathrm{cm}$, then the altitude of the bigger triangle in centimetres, is:

In a $\Delta ABC, DE$ is parallel to $BC$ where $D$ and $E$ are the points on $AB$ and $AC$, respectively and $AD = 4$ cm, $DB = 8$ cm, $AE = 3$ cm. Length of $EC$ is:

In $∆\mathrm{ABC}, \mathrm{D}$ and $\mathrm{E}$ are the points on sides $\mathrm{AB}$ and $\mathrm{BC}$ respectively such that $\mathrm{DE}\parallel \mathrm{AC}$. If $\mathrm{AD}:\mathrm{DB}=5:3$, then what is the ratio of the area of $∆\mathrm{BDE}$ to that of the trapezium $\mathrm{ACED}$?