Question

The construction of a triangle ABC, given that BC = 4 cm, $\angle B={30}^{\circ },$ is not possible when difference of AB and AC is equal to

• A.
  3 cm
• B.
  3.5 cm
• C.
  2 cm
• D.
  4 cm

Answer 1

The correct option is D

4 cm


First of all, we draw a rough triangle ABC, One of the base angle is given ${30}^{\circ }.$ Base length BC is given 4cm .

We can represent the difference of remaining two sides as AB-AC

we do not know either AB>AC or AC > AB

Let us take the difference of other two sides is equal to 3cm ; In this case, we can construct the triangle with the given information, as

by inequality of triangles.
We know that
"The difference of any two sides of a triangle is always less than the third side. "

So, If we consider, $AB-ACorAC-AB=3\Rightarrow <\text{Third sides i.e=BC,}$

So, in this case, triangle can be constructed.

$\Rightarrow$ similarly, If we take the difference of two sides as 3.5 cm.
We are again getting the difference of two sides is less than the third side that means we can construct the triangle.

$\Rightarrow$ Similarly, in Option (c), as 2<4.

$\Rightarrow$ But when we take the Option (d).
BC = 4 cm.
Now, the concept that the difference o two sides of a triangle is always less than the third side is contradicted.

$\Rightarrow$Therefore Option (d) 4 cm is the correct answer.