7 centimeters is a possible length for the third side ⇒ B
Step-by-step explanation:
Let us revise the triangle Inequality Theorem
- The sum of the lengths of any 2 sides of a triangle must be greater than the length of the third side
- To prove that by easy way add the smallest two sides, if their sum greater than the third side,then the sides can form a triangle
Assume that the length of the third side is x cm
∵ The length of two sides are 7 cm and 10 cm
∵ The length of the third side is x cm
- Put the sum of x and 7 greater than 10 ( x and 7 are the smallest sides)
∴ x + 7 > 10
- Subtract 7 from both sides
∴ x > 3
- Put the sum of 7 and 10 greater than x (7 and 10 are the smallest sides)
∵ 7 + 10 > x
∴ 17 > x
∴ x < 17
- By using one inequality for x (combined the two inequalities in one)
∴ 3 < x < 17
That means the length of the third side is any number between 3 and 17
There is only one answer between 3 and 17
∵ 7 is between 3 and 17
∴ The length of the third side could be 7 cm
7 centimeters is a possible length for the third side
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