Which set of numbers can represent the side lengths, in inches, of an acute triangle? 4, 5, 7 5, 7, 8 6, 7, 10 7, 9, 12

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4 5 7

Step-by-step explanation:

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Set B i. e., 5, 7, 8 represent the side of acute angled triangle.

Step-by-step explanation:

Given: Set of numbers.

To find: Set that represent sides of an acute angled traingle.

We use the following result:

When given 3 triangle sides then to determine if the triangle is acute angled, right angled or obtuse angled.

First find Square all 3 sides, then Sum the squares of the 2 shortest sides and then Compare the sum to the square of the last side.

if sum > Square of last side ⇒ it is Acute Triangle

if sum = Square of last side ⇒ it is Right Triangle

if sum < Square of last side ⇒ it is Obtuse Triangle

a). 4, 5, 7

4² = 16, 5² = 25, 7² = 49

16 + 25 = 41

∵ 41 < 49

⇒ It is an Obtuse Traingle.

b). 5, 7, 8

5² = 25, 7² = 49, 8² = 64

25 + 49 = 74

∵ 74 > 64

⇒ It is an acute Triangle.

c). 6, 7, 10

6² = 36, 7² = 49, 10² = 100

36 + 49 = 85

∵ 85 < 100

⇒ It is an Obtuse Triangle.

d). 7, 9, 12

7² = 49, 9² = 81, 12² = 144

49 + 81 = 130

∵ 130 < 144

⇒ It is an Obtuse Triangle.

Therefore, Set B i. e., 5, 7, 8 represent the side of acute angled triangle.