Question

two of a triangles side lengths are 8 cm and 8 cm. which of the following side lengths is a possible length of the third side? 15 cm 16 cm 17 cm 18 cm two of a triangles side lengths are 20 cm and 28 cm. what is the smallest possible whole number length of the third side? your answer

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\).

Step2: For the first triangle with \(a = 8\) and \(b = 8\)

Calculate \(a + b=8 + 8=16\) and \(|a - b|=|8 - 8| = 0\). So \(0\lt x\lt16\). Among the options \(15\mathrm{cm}\), \(16\mathrm{cm}\), \(17\mathrm{cm}\), \(18\mathrm{cm}\), only \(15\mathrm{cm}\) satisfies this inequality.

Step3: For the second triangle with \(a = 20\) and \(b = 28\)

Calculate \(|a - b|=|20 - 28|=8\) and \(a + b=20 + 28 = 48\). The inequality for the third - side length \(x\) is \(8\lt x\lt48\). The smallest whole - number value of \(x\) that satisfies this inequality is \(9\).

Answer:

1. A. \(15\mathrm{cm}\)
2. \(9\)