Question

Suppose we want to draw a triangle with one side 6 centimeters long. Which of the following pairs of lengths can be the lengths of the other two sides?

(i) 4 cm, 1 cm

(ii) 4 cm, 2 cm

(iii) 4 cm, 3 cm

(iv) 5 cm, 10 cm

(v) 5 cm, 11 cm

(vi) 5 cm, 12 cm

Answer 1

(i) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 4 cm and 1 cm centred at A and B, respectively.

We can observe that the circles do not intersect each other, so 6 cm, 4 cm and 1 cm are not the lengths of the sides of the required triangle.

(ii) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 4 cm and 2 cm centred at A and B, respectively.

We can observe that the circles do not intersect each other, so 6 cm, 4 cm and 2 cm are not the lengths of the sides of the required triangle.

(iii) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 4 cm and 3 cm centred at A and B, respectively.

We can observe that the circles intersect each other at a point, say, C.

Step 3: Join AC and BC.

Thus, 6 cm, 4 cm and 3 cm are the lengths of the sides of the required triangle ABC.

(iv) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 5 cm and 10 cm centred at A and B, respectively.

We can observe that the circles intersect each other at point C.

Step 3: Join AC and BC.

Thus, 6 cm, 5 cm and 10 cm are the lengths of the sides of the required triangle ABC.

(v) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 5 cm and 11 cm centred at A and B, respectively.

We can observe that the circles do not intersect each other, so 6 cm, 5 cm and 11 cm are not the lengths of the sides of the required triangle.

(vi) To check whether we can construct a triangle with the given measurements or not, we need to do the following constructions.

Step 1: Draw a line segment AB of length 6 cm.

Step 2: Draw two circles of radii 5 cm and 12 cm centred at A and B, respectively.

We can observe that the circles do not intersect each other, so 6 cm, 5 cm and 12 cm are not the lengths of the sides of the required triangle.