Chapter 8, Problem 12CR

To determine

To find: Whether the triangle formed with sides having lengths $2\sqrt{3},2\sqrt{3},6$ named is acute, right, or obtuse.

Answer to Problem 12CR

The triangle is obtuse.

Explanation of Solution

Given information:

Length of the sides are $2\sqrt{3},2\sqrt{3},6$ .

Since $2\sqrt{3}+2\sqrt{3}\approx 6.93>6$

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 ${\left(2\sqrt{3}\right)}^2+{\left(2\sqrt{3}\right)}^2=12+12$

$=24\text{}<36=6^2$

$\therefore {\left(2\sqrt{3}\right)}^2+{\left(2\sqrt{3}\right)}^2<{\left(6\right)}^2$

Hence, the triangle is obtuse.