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How do I use the side lengths, determine what type of triangle would be created, if any?

How do I use the side lengths, determine what type of triangle would be created, if-example-1
User Viniciusalvess
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1 Answer

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Answer

2, 4, 5 (Obtuse Triangle)

3, 4, 5 (Right angle triangle)

6, 7, 8 (Acute Triangle)(

7, 9, 15 (Obtuse Triangle)

Step-by-step explanation

To answer this question, we first explain what these type of triangles are

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

If the three sides in a triangle are a, b and c with c being the longest side.

When

c² < a² + b²

The triangle is an acute triangle.

When

c² = a² + b²

The triangle is a right angle triangle.

When

c² > a² + b²

The triangle is an obtuse triangle.

But, it should be noted that if the longest side is equal to or more than the sum of the two sides, c ≥ a + b, the triangle is not possible.

So, taking these given side lengths one at a time,

2, 4, 5

a = 2, b = 4, c = 5

a² + b² = 2² + 4² = 4 + 16 = 20

c² = 5² = 25

25 > 20

c² > a² + b²

This triangle is an obtuse triangle.

3, 4, 5

a = 3, b = 4, c = 5

a² + b² = 3² + 4² = 9 + 16 = 25

c² = 25

25 = 25

c² = a² + b²

This triangle is a right angle triangle.

6, 7, 8

a = 6, b = 7, c = 8

a² + b² = 6² + 7² = 36 + 49 = 85

c² = 8² = 64

64 < 85

c² < a² + b²

This triangle is an acute triangle.

7, 9, 15

a = 7, b = 9, c = 15

a² + b² = 7² + 9² = 49 + 81 = 130

c² = 15² = 225

225 > 130

c² > a² + b²

This triangle is an obtuse triangle.

Hope this Helps!!!

User Ewalshe
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