# The construction of a ΔABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to

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The construction of a ΔABC, given that BC = 3 cm, ∠C = 60° is possible when difference of AB and AC is equal to
(a) 3.2 cm
(b) 3.1 cm
(c) 3 cm
(d) 2.8 cm

answered Feb 2, 2018 by Expert (1,417 points)
(d) Given, BC = 3 cm and ∠C=60°
We know that, the construction of a triangle is possible, if sum of two sides is greater than the third side of the triangle i.e.,
AB+ BC > AC
⇒  BC > AC – AB
⇒  3 > AC – AB
So, if AC – AB = 2.8 cm, then construction of ΔABC with given conditions is possible.

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