Scalene Triangle Practice Problems and Exercises

Master scalene triangles with step-by-step practice problems. Learn to identify and solve scalene triangle exercises with detailed solutions and examples.

📚What You'll Practice with Scalene Triangles
  • Identify scalene triangles by examining side lengths and properties
  • Distinguish scalene triangles from isosceles and equilateral triangles
  • Calculate perimeter and area of scalene triangles using given measurements
  • Solve real-world problems involving scalene triangle applications
  • Apply triangle inequality theorem to verify scalene triangle existence
  • Classify triangles based on side lengths and angle measures

Understanding Scalene triangle

Complete explanation with examples

Definition of Scalene Triangle

An scalene triangle is a triangle that has all its sides of different lengths.

Detailed explanation

Practice Scalene triangle

Test your knowledge with 20 quizzes

Is the triangle in the drawing an acute-angled triangle?

Examples with solutions for Scalene triangle

Step-by-step solutions included
Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer:

Right triangle

Video Solution
Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer:

Obtuse Triangle

Video Solution
Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer:

Equilateral triangle

Video Solution

Frequently Asked Questions

What is a scalene triangle and how do I identify one?

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A scalene triangle is a triangle where all three sides have different lengths. To identify one, measure or compare all three sides - if no two sides are equal, it's a scalene triangle.

What's the difference between scalene, isosceles, and equilateral triangles?

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• Scalene triangle: All three sides have different lengths • Isosceles triangle: Two sides have equal lengths • Equilateral triangle: All three sides have equal lengths

How do you find the perimeter of a scalene triangle?

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To find the perimeter of a scalene triangle, add all three side lengths together. Since all sides are different, you simply calculate: Perimeter = side a + side b + side c.

Can a scalene triangle be a right triangle?

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Yes, a scalene triangle can be a right triangle. A triangle can be classified by both its sides (scalene, isosceles, equilateral) and its angles (acute, right, obtuse) independently.

What are some real-world examples of scalene triangles?

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Real-world scalene triangles include: 1. Roof trusses in construction 2. Triangular road signs with unequal sides 3. Mountain peaks viewed from the side 4. Sail shapes on boats

How do you prove three sides can form a scalene triangle?

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Use the triangle inequality theorem: the sum of any two sides must be greater than the third side. Check all three combinations: a+b>c, a+c>b, and b+c>a.

What formulas work for calculating scalene triangle area?

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For scalene triangles, you can use: • Heron's formula: √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 • Base × height ÷ 2 (if height is known) • ½ab sin(C) using two sides and included angle

Are scalene triangles harder to work with than other triangles?

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Scalene triangles require more careful calculation since no sides or angles are equal, but they follow the same geometric principles. With practice, solving scalene triangle problems becomes straightforward.

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