Question

Which of the following set of measurements will form a triangle

• A. $11cm,4cm,6cm$
• B. $13cm,14cm,25cm$
• C. $8cm,4cm,3cm$
• D. $5cm.16cm.5cm$

Answer 1

The correct option is B $13cm,14cm,25cm$

Triangle Inequality Theorem states that the sum of two side lengths of a triangle is always greater than the third side.

If this is true for all three combinations of added side lengths.

i.e. $a+b>c,$ $b+c>a$ and $c+a>b$ then the lengths form a triangle

(A) $11+4=15>6$

And $4+6=10\ngtr 11$

So, it does not form a triangle

(B) $13+14=27>25$

And $14+25=39>13$

And $25+13=38>14$

So, it forms a triangle

(C) $8+4=12>3$

And $8+3=11>4$

And $4+3=7\ngtr 8$

So, it does not form a triangle

(D) $5+16=21>5$

And $5+5=10\ngtr 16$

So, it does not form a triangle.

Hence option B is the correct answer