Question

The construction of a triangle ABC, given that BC = 6 cm, B = 45° is not possible when difference of AB andAC is equal to:​

Answer 1

Answer:

Given, BC = 6 cm and ∠B= 45°

Given, BC = 6 cm and ∠B= 45°We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.

Given, BC = 6 cm and ∠B= 45°We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.i.e., AB + BC < AC

Given, BC = 6 cm and ∠B= 45°We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.i.e., AB + BC < AC⇒ BC < AC – AB

Given, BC = 6 cm and ∠B= 45°We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.i.e., AB + BC < AC⇒ BC < AC – AB⇒ 6 < AC-AB

Given, BC = 6 cm and ∠B= 45°We know that, the construction of a triangle is not possible, if sum of two sides is less than or equal to the third side of the triangle.i.e., AB + BC < AC⇒ BC < AC – AB⇒ 6 < AC-ABSo, if AC – AB= 6.9 cm, then construction of ΔABC with given conditions is not possible.

Answer 2

The Construction of such Triangle ABC would not be physically possible if the difference in length of the sides AB and AC is greater than the length of BC.

1) Here length of BC is 6 cm.

2) Hence we can not have | AB - BC| > 6 cm.

3) Also for  | AB - BC| = 6 cm, the triangle can not be constructed