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The construction of a ∆ABC in which AB = 4 cm, ∠A = 60° is not possible when difference of BC and AC is equal to [NCERT Exemplar]
(a) 3.5 cm
(b) 4.5 cm
(c) 3 cm
(d) 2.5 cm
Answers
Answer:
(b) 4.5 cm
Step-by-step explanation:
Here,
As we know that the sum of any two sides of a triangle is always greater than the third side.
Similarly, the difference of any two side of a triangle is always less than the third side.
And as per the options only 4.5>4 which is not possible.
Hence the answer is (b) 4.5 cm
Answer:
(b) 4.5 cm
Step-by-step explanation:
The Triangle Inequality refers to the fact that the sum of the lengths of two sides of a triangle is greater than the third side. This is really just saying that the straight line between points (i.e. the "third side") is the shortest route between those two points.
So in ΔABC, we must have
AC + AB > BC.
Subtracting AC from both sides, this means we must have
AB > BC - AC
Since we are given that AB = 4 cm, we must have
4 cm > BC - AC.
In particular, it is not possible to have BC - AC = 4.5 cm.
Hope that helps.