Chapter 8, Problem 12CT

To determine

To find: Whether the triangle formed with sides having lengths $\frac{3}{5},\frac{4}{5},1$ named is acute, right, or obtuse.

Answer to Problem 12CT

The triangle is right angle.

Explanation of Solution

Given information:

Length of the sides are $\frac{3}{5},\frac{4}{5},1$ .

Since $\frac{3}{5}+\frac{4}{5}=\frac{7}{5}>1$

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 ${\left(\frac{3}{5}\right)}^2+{\left(\frac{4}{5}\right)}^2=\frac{9}{25}+\frac{16}{25}$

$\begin{array}{l}=\frac{25}{25}\\ \Rightarrow {\left(\frac{3}{5}\right)}^2+{\left(\frac{4}{5}\right)}^2=1^2={\left(\text{third}\text{side}\right)}^2\end{array}$

$\therefore {\left(\frac{3}{5}\right)}^2+{\left(\frac{4}{5}\right)}^2={\left(\text{third}\text{side}\right)}^2$

Hence, the triangle is right angle.