Question

A triangle can be constructed by taking its sides as:

• A. $1.8cm,2.6cm,4.4cm$
• B. $2cm,3cm,4cm$
• C. $2.4cm,2.4cm,6.4cm$
• D. $3.2cm,2.3cm,5.5cm$

Answer 1

The correct option is B $2cm,3cm,4cm$

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than (not equal to) the length of the third side.

For example:- If $A,B$ and $C$ are the sides of a triangle then, a triangle can only be constructed when :

$A+B>C$

$A+C>B$

$B+C>A$

So, here each option can be easily verified to check its feasibility to make a triangle:

(A)

$1.8+2.6>4.4$ ..... [Doesn't Satisfies]

$1.8+4.4>2.6$ ..... Satisfies

$2.6+4.4>1.8$ ..... Satisfies

(B)

$2+3>4$ ..... Satisfies

$2+4>3$ ..... Satisfies

$3+4>2$ ..... Satisfies

(C)

$2.4+2.4=4.8>6.4$ ..... [Doesn't Satisfies]

$2.4+6.4=9.0>6.4$ ..... Satisfies

(D)

$3.2+2.3=5.5>5.5$ ..... [Doesn't Satisfies]

Hence, option B is correct and its sides can be used to construct a triangle.