Scalene Triangle Definition

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Scalene triangle is a triangle in which none of the sides of the triangle are equal to each other. This also means that all the three angles in a scalene triangle are not equal to each other and therefore are of different measure. Sum of all the three angles in any triangle is equal to 180º and hence this rule even applies to a scalene triangle. The sum of all the sides of the scalene triangle gives the perimeter of the scalene triangle.

Example 1: The angles in triangle ABC are (x + 40)º, (x + 30)º and (3x + 20)º. Is ABC a scalene triangle?

Sum of the angles in a triangle = 180º

So x+ 40+ x+ 30+ 3x+ 20= 180º

5x+ 90= 180º

5x= 180º - 90==> 5x= 90==> x= 90/5 = 18

This gives: (x + 40) = 18 + 40= 58º

(x + 30) = 18 + 30= 48º

(3x + 20)= 54 + 20= 74º

Since the angles in triangle ABC are not equal to each other, therefore ABC is a scalene triangle.

Example 2: Perimeter of triangle PQR of side lengths, (x+ 2), (x+ 5) and (x+ 9) is 52m. Is triangle PQR a scalene triangle?

Perimeter of a triangle = Sum of all the sides of the triangle

So, (x+ 2)+ (x+ 5)+ (x+ 9)= 52

So, 3x + 16 = 52

3x= 52- 16==> 3x = 36==> x = 36/3 = 12.

Therefore the sides are: x+ 2= 12+ 2= 14m

x+ 5= 12+ 5= 17m

x+ 9= 12+ 9= 21m

Since the length of the sides are different, hence triangle PQR is a scalene triangle.

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