Question

The length of all sides of triangle $ABC$ are in integral units. If $l\left(AB\right)=10$ units and $l\left(BC\right)=15$ units, the number of distinct possible values for $l\left(AC\right)$ are

• A. $5$
• B. $19$
• C. $25$
• D. $21$

Answer 1

The correct option is B $19$

Consider the property for a triangle,

Sum of two sides of a triangle $>$ third side

In $△ABC$,

$AB=10$ $BC=15$ $AC=x$

Using above mentioned property,

$10+15>x$ $⟹25>x$ $⟹x<25$

$15+x>10$ $⟹x>-5$ $⟹x>0$

$10+x>15$ $⟹x>5$ $⟹5<x$

Combining we get: $5<x<25$

Integral values of, $x=6,7,8,9,10,\dots ..,24=19$ values

Option B