Question

if the lengths of two sides of a triangle are 7 and 10, the length of the third side may be
4
1
3
2

Explanation:

Step1: Recall triangle inequality theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side, and the difference of the lengths of any two sides must be less than the length of the remaining side. Let the length of the third side be \(x\). Then we have two inequalities: \(10 - 7 < x\) and \(x < 10 + 7\).

Step2: Calculate the range of \(x\)

First, calculate \(10 - 7 = 3\) and \(10 + 7 = 17\). So the length of the third side \(x\) must satisfy \(3 < x < 17\).

Step3: Check the options

• For 4: Since \(3 < 4 < 17\), 4 satisfies the inequality.
• For 1: Since \(1

ot> 3\), 1 does not satisfy.

• For 3: Since \(3\) is not greater than \(3\) (the inequality is strict), 3 does not satisfy.
• For 2: Since \(2

ot> 3\), 2 does not satisfy.

Answer:

4