In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x - 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.

Two triangles are similar if their corresponding sides are ___.

Perimeters of two similar triangles are 27 cm and 16 cm. If the length of a side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle

In trapezium ABCD, BC ∥ AD and AD = 4 cm. Diagonals AC and BD meet at O such that AO/OC = DO/OB = 1/2. Find the length of BC.

DE ∥ BC of ΔABC where D and E are two points on AB and AC, respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, calculate the length of AC.

In the given figure, AC ∥ DE ∥ BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm and BF = 30 cm: (a) Prove △GED ∼ △GBF (b) Find DE (c) Find DB : AB.

The areas of two similar triangles are in the ratio 9 : 64. The ratio of their corresponding altitudes is: (a) 3 : 8 (b) 2 : 1 (c) 9 : 64 (d) 8 : 3

In the given figure, ∠BAP = ∠DCP = 70°, PC = 6 cm and CA = 4 cm. Then PD : DB is: (a) 5 : 3 (b) 3 : 5 (c) 3 : 2 (d) 2 : 3

In the given diagram, DE ∥ BC and AD : DB = 2 : 3. (a) Prove that: ΔADE ~ ΔABC and hence find DE : BC. (b) Prove: ΔDFE ~ ΔCFB. (c) Given, area of ΔDFE = 16 square units, find the area of ΔCFB.

In the given diagram, △ABC ∼ △PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively, then: (a) △ABC ∼ △PQS (b) △ABD ∼ △PQS (c) △ABD ∼ △PSR (d) △ABC ∼ △PSR

In the given diagram, △ABC ∼ △EFG. If ∠ABC = ∠EFG = 60°, then the length of side FG is: (a) 15 cm (b) 20 cm (c) 25 cm (d) 30 cm

In △ABC, ∠ABC = 90°, AB = 20 cm and AC = 25 cm. DE is perpendicular to AC such that ∠DEA = 90° and DE = 3 cm, as shown. (a) Prove that △ABC ∼ △AED. (b) Find BC, AD and AE. (c) If BCED represents land on a map whose actual area is 576 m², find the scale factor of the map.