Chapter 8, Problem 10CT

To determine

To find: Whether the triangle formed with sides having lengths $11,12,13$ named is acute, right, or obtuse.

Answer to Problem 10CT

The triangle is acute.

Explanation of Solution

Given information:

Length of the sides are $11,12,13$ .

Since $11+12=23>13$

Thus, the sum of two sides greater than the third side.

Therefore, the triangle formed with given lengths.

And also we know that if $a,b,c$ are lengths of three sides of a triangle then

$i.$ The triangle is said to be right angle triangle, if $a^2+b^2=c^2$

$ii.$ The triangle is said to be obtuse triangle, if $a^2+b^2<c^2$

$iii.$ The triangle is said to be acute triangle, if $a^2+b^2>c^2$

From given lengths, we observe that ${11}^2+{12}^2=121+144$

  $=265>169={13}^2$

$\therefore {11}^2+{12}^2>{13}^2$

Hence, the triangle is acute.