Step-by-step explanation:

1.Draw a line segment XY of length 4.5cm

2.Taking 6cm as radius, and X as center, draw an arc.

3.Taking 5cm as radius, and Y as center, draw another arc.

4.Let Z be the point where the two arcs intersect.

Join XZ and YZ and label the sides.

Thus,△XYZ is the required triangle.

Answer:

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(i) No. It is not possible to construct a triangle with lengths of its sides 5 cm,4 cm and 9 cm because the sum of two sides is not greater than the third side i.e. 5+4 is not greater than 9.

(ii) Yes. It is possible to construct a triangle with lengths of its sides 8 cm,7 cm and 4 cm because the sum of two sides of a triangle is greater than the third side.

(iii) Yes. It is possible to construct a triangle with lengths of its sides 10 cm,5 cm and 6 cm because the sum of two sides of a triangle is greater than the third side.

(iv) Yes. It is possible to construct a triangle with lengths of its sides 2.5 cm,5 cm and 7 cm because the sum of two sides of a triangle is greater than the third side.

(v) No. It is not possible to construct a triangle with lengths of its sides 3 cm,4 cm and 8 cm because the sum of two sides is not greater than the third side.

Step-by-step explanation: