A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac{3}{5}\) of the corresponding sides of the triangle PQR (scale factor \(\frac { 3 }{ 5 } <1\)) 

Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac { 7 }{ 4 } \) of the corresponding sides of the triangle PQR (scale factor \(\frac { 7 }{ 4 } \)>1)

A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamp post. The girl whose height is 12.5 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamp post are in a same line, find the height of the lamp post.

Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.

Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac { 2 }{ 3 } \) of the corresponding sides of the triangle PQR (scale factor \(\frac { 2 }{ 3 } <1\)).

Construct a triangle similar to a given triangle ABC with its sides equal to \(\frac { 6 }{ 5 } \) of the corresponding sides of the triangle ABC (scale factor \(\frac { 6 }{ 5 } >1\)).

Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac { 7 }{ 3 } \) of the corresponding sides of the triangle PQR (scale factor\(\frac { 7 }{ 3 } >1\))

In \(\triangle\) ABC, if DE||BC, AD = x, DB = x − 2, AE = x +2 and EC = x − 1 then find the lengths of the sides AB and AC.

In the figure DE||AC and DC||AP. Prove that \(\frac { BE }{ CE } =\frac { BC }{ CP } \)