Question

The sides of a triangle have lengths$(\mathrm{in}\mathrm{cm})10,6.5\mathrm{and}\mathrm{a},$where $\mathrm{a}$ is a whole number. The minimum value that a can take is-

• A. $6$
• B. $5$
• C. $3$
• D. $4$

Answer 1

The correct option is D

$4$

From the given details the two sides are given, $10\mathrm{and}6.5.$

We know that from Triangle Inequality Theorem the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

So,

$$\begin{gathered} 6.5+\mathrm{a}=10 \\ \mathrm{a}>10–6.5 \\ \mathrm{a}>3.5\cong 4 \end{gathered}$$

Hence the answer is$\left(\mathrm{d}\right)4$