Question

The construction of the triangle ABC is possible if it is given that BC = 4 cm, ∠C = 60° and the difference of AB and AC is
(i) 3.5 cm
(ii) 4.5 cm
(iii) 3 cm
(iv) 2.5 cm

Answer 1

Answer:

4.5 is the answer

as difference of two sides is less than third side

Answer 2

Given:

• BC = 4 cm
• ∠C = 60°

To Find:

• Difference between AB and AC

Solution:

• We can construct a triangle only if the two sides of a triangle are measured are greater than the other one side.
• AB+BC>AC
• Rearranging the above mentioned inequality to find the difference between AB and AC
• We get, BC>AC-AB
• 4>AC-AB, (BC = 4cm)
• By the above inequality, we get to know that when AC-BC is 2.5 cm we can construct a triangle with ∠C = 60°

The answer is 2.5 cm. (option iv)