Triangles questions for CBSE X

A 1.6 m tall girl stands 3.2 m from a lamp-post and casts a 4.8 m shadow on level ground. Find the lamp height.

If AB/DE=BC/FD in triangles ABC and DEF, which included-angle equality establishes SAS similarity?

D lies on AB and E on AC of triangle ABC, with AD/DB=AE/EC. ∠ADE=70°, ∠BAC=50°. Find ∠BCA.

A line DE parallel to BC intersects AB and AC of triangle ABC at D,E. Which ratio follows from the basic proportionality theorem?

L lies on AC, M on AB, N on AD, with LM∥CB and LN∥CD. Which ratio equals AN/ND?

Diagonals AC and BD of trapezium ABCD, AB∥CD, meet at O. If AB=2CD, find area(AOB):area(COD).

ABC∼DEF with areas 64 cm² and 121 cm². If EF=15.4 cm, find corresponding side BC.

In triangle ABC, D is on AB,E on AC, and DE∥BC. If BC=8 cm,AB=6 cm,AD=1.5 cm, find DE.