Chapter 3.6, Problem 1PSA

To determine

To find that the triangle given is scalene, isosceles or equilateral.

Answer to Problem 1PSA

Given triangle EFG is a scalene triangle

Explanation of Solution

Given information:

Perimeter of given triangle is 32 units

Sides of given triangle are 10, x + 7 and 2x − 3

Formula used:

Perimeter of triangle = sum of measures of all its sides

Scalene triangle has all sides unequal

Isosceles triangle ha two sides equal

Equilateral triangle has all sides equal

Calculation:

Since perimeter of triangle = sum of measures of its sides

  $\therefore$ Perimeter of given triangle EFG

  $\begin{array}{l}=\text{EF + FG + GE}\\ \text{=}\left(2\text{x}-\text{3}\right)+\left(\text{x + 7}\right)+10\\ =3\text{x + 14 units}\mathrm{........}\left(i\right)\end{array}$

Given that

Perimeter of triangle EFG = 32 units

  $\therefore$ from (i), we have

  $\begin{array}{l}\text{3x + 14 = 32}\\ \Rightarrow \text{3x = 32 }-\text{ 14=18}\\ \Rightarrow \text{x=}\frac{18}{3}=6\end{array}$

  $\begin{array}{l}\therefore \text{Sides of the given triangle EFG will be}\\ \text{GE = 10 units }\mathrm{....}\text{given}\\ \text{EF= 2x }-\text{ 3=2}\times 6-3=12-3=9\text{units}\\ \text{and GF = x + 7= 6+ 7 = 13 units}\end{array}$

Since, all the sides of the given triangle are unequal in size

  $\therefore$ Given triangle EFG is a scalene triangle.