Question

11
multiple choice 2 points
two sides of a triangle are 4cm and 11cm. the third side must be ________.
between 4cm and 7cm
greater than 11cm
between 7cm and 15cm
less than 4cm

Explanation:

Step1: Apply triangle side - length rule

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. Let the two given sides be \(a = 4\mathrm{cm}\) and \(b=11\mathrm{cm}\), and the third side be \(c\). Then \(b - a\lt c\lt b + a\).

Step2: Calculate the range

Substitute \(a = 4\mathrm{cm}\) and \(b = 11\mathrm{cm}\) into the inequality. \(11-4\lt c\lt11 + 4\), which simplifies to \(7\mathrm{cm}\lt c\lt15\mathrm{cm}\).

Answer:

C. between \(7\mathrm{cm}\) and \(15\mathrm{cm}\)