# In each of the following cases, given reasons to show that the construction of ∆ABC is not possible:

Question:

In each of the following cases, given reasons to show that the construction of ∆ABC is not possible:
(i) AB = 6 cm, ∠A = 40° and (BC + AC) = 5.8 cm.
(ii) AB = 7 cm, ∠A = 50° and (BC – AC) = 8 cm.
(iii) BC = 5 cm, ∠B = 80°, ∠C = 50° and ∠A = 60°.
(iv) AB = 4 cm, BC = 3 cm and AC = 7 cm.

Solution:

(i) AB = 6 cm, ∠A = 40° and (BC + AC) = 5.8 cm.
Here BC + AC is not greater than AB so, this triangle is not possible.

(ii) AB = 7 cm, ∠A = 50° and (BC – AC) = 8 cm.
Here BC – AC is not less than AB so this triangle is not possible.

(iii) BC = 5 cm, ∠B = 80°, ∠C = 50° and ∠A = 60°.
Sum of the angles of the given triangle is not equal to 180°">°° so, given triangle is not possible.

(iv) AB = 4 cm, BC = 3 cm and AC = 7 cm.
Sum of two sides of this triangle not greater than third side so given triangle not possible.