List of top Mathematics Questions on Similarity of Triangles asked in Maharashtra Class X Board

If DE : BC = 3 : 5, then find A($\triangle$ADE) : A($\square$DBCE).

In the following figure DE$||$BC, then: If DE = 4 cm, BC = 8 cm, A($\triangle$ADE) = 25 cm$^2$, find A($\triangle$ABC).

In the following figure $\angle$MNP = 90$^\circ$, seg NQ $\perp$ seg MP, MQ = 9, QP = 4, find NQ.

Solve the following sub-questions (any four): In $ \triangle ABC $, $ DE \parallel BC $. If $ DB = 5.4 \, \text{cm} $, $ AD = 1.8 \, \text{cm} $, $ EC = 7.2 \, \text{cm} $, then find $ AE $.

In the following figure, XY $||$ seg AC. If 2AX = 3BX and XY = 9. Complete the activity to find the value of AC.

Activity:
2AX = 3BX (Given)
\[\therefore \frac{AX}{BX} = \frac{3}{\boxed{2}} \ \\ \frac{AX + BX}{BX} = \frac{3 + 2}{2} \quad \text{(by componendo)} \ \\ \frac{BA}{BX} = \frac{5}{2} \quad \dots \text{(I)} [6pt] \\ \text{Now } \triangle BCA \sim \triangle BYX ; (\boxed{\text{AA}} \text{ test of similarity}) [4pt] \\ \therefore \frac{BA}{BX} = \frac{AC}{XY} \quad \text{(corresponding sides of similar triangles)} [4pt] \\ \frac{5}{2} = \frac{AC}{9} \quad \text{from (I)} [4pt] \\ \therefore AC = \boxed{22.5}\]

If $ \triangle ABC \sim \triangle PQR $ and $ AB : PQ = 2 : 3 $, then find the value of $ \frac{A(\triangle ABC)}{A(\triangle PQR)} $:

If $\triangle ABC \sim \triangle PQR$ and $\dfrac{A(\triangle ABC)}{A(\triangle PQR)} = \dfrac{16}{25}$, then find $AB : PQ$.

In $\triangle ABC$, seg $DE \parallel BC$. If $2A(\triangle ADE) = A(\triangle DBCE)$, find $AB : AD$ and show that $BC = \sqrt{3 \, DE$.}