Question

question 36 of 45 the legs of a triangle measure 13 centimeters and 17 centimeters. which of the following is the measure for the longest side of the triangle? a. 29 cm b. 4 cm c. 31 cm d. 30 cm

Explanation:

Step1: Recall triangle - side rule

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the two given sides be \(a = 13\) cm and \(b=17\) cm. Let the third - side be \(c\). Then \(a + b>c\), \(a + c>b\), and \(b + c>a\). Also, for \(c\) to be the longest side, \(c>a\) and \(c>b\). Since \(a + b=13 + 17=30\) cm, the length of the longest side \(c\) must be less than \(a + b\) (i.e., \(c<30\) cm) and greater than \(17\) cm.

Step2: Check each option

• Option A: \(29\) cm. Since \(17<29<30\), this option satisfies the triangle - side rule for the longest side.
• Option B: \(4\) cm. Since \(4<13\) and \(4<17\), it cannot be the longest side.
• Option C: \(31\) cm. Since \(31>30\) (\(13 + 17\)), it does not satisfy the triangle - side rule.
• Option D: \(30\) cm. The sum of the two given sides is \(30\) cm, and the third - side must be less than the sum of the other two sides, so \(30\) cm does not satisfy the triangle - side rule.

Answer:

A. 29 cm