, 18.05.2020christiandumanon

If a triangle has side lengths of 22 32 and 55 units respectively what type of triangle is it? Acute Obtuse Right or no solution

Classifications of Triangles according to the measure of the sides is the type of triangle, right?

Well, it was scalene triangle.

Explanation: A scalene triangle has three sides with different lengths. The sides are not congruent, since they have different lengths.

scalene triangle

Step-by-step explanation:

Scalene triangle are triangles that have no congruent or equal sides. The units of the side lengths of the triangle asked are 22, 32 and 55 units. There is no similar units and the 3 have different measurements therefore it is scalene triangle.

Step-by-step explanation:

To determine if the given sides measurements form a triangle, use the Triangle Inequality Theorem where the sum of the lengths of any two sides of a triangle is greater than the third side.

Let's say a, b and c are side, then:

a + b > ca + c > bb + c > a

The condition must satisfy all sides of the triangle.

Let:

a = 22b = 32c = 55

Determine if the given sides form a triangle:

a + b > c

22 + 32 > 55

54 > 55  NOT TRUE

a + c > b

22 + 55 > 32

77 > 32  TRUE

b + c > a

32 + 55 > 22

87 > 22 TRUE

The inequality condition must satisfy any side, but since 54 > 55  is NOT TRUE, therefore the given side lengths  do not form a triangle.

To determine the type of triangle, use the Pythagorean Inequality Theorem where if a, b and c are sides of the triangle:

Right Triangle: c² = a² + b²Acute Triangle:  c² < a² + b²Obtuse Triangle:  c² > a² + b²

Use Pythagorean Inequality Theorem:

(55)² = (22)² + (32)²

3,025 = 484 + 1,024

3,025 > 1,508  could be an obtuse triangle but THIS IS NOT TRUE for this particular problem because  it has been determined by the triangle inequality that the given sides 22, 32, and 55 do not form a triangle.

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