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The construction of ΔABC, given that BC = 6 cm, ∠B = 45° is not possible when difference of AB and AC is equal to
(a) 6.9 cm
(b) 5.2 cm
(c) 5.0 cm
(d) 4.0 cm
(a) 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
So, if AC – AB= 6.9 cm, then construction of ΔABC with given conditions is not possible.