Question

Choose the correct answer from the alternatives given.
If two sides of an acute angled triangle are $8$ cm and $15$ cm and the length of third side is x. then

• A. $13<x<17$
• B. $7<x<17$
• C. $\sqrt{161}$ < x < $17$
• D. $7<x<23$

Answer 1

The correct option is C $\sqrt{161}$ < x < $17$

If x be greatest side then $x^2<8^2+{15}^2$
$x^2<289$ $\Rightarrow$ $x<17$
If x be smallest side then ${15}^2<8^2+x^2$
$x^2$ > $225-64$
$x^2$ > $161$
x > $\sqrt{161}$
$\sqrt{161}$ < x < $17$