Question

drag a vertex of the triangle to change its shape. double - click or double - tap a vertex or side to prevent it from changing. what are the possible measures of the triangles sides? choose three correct answers. 3, 4, 5 9, 12, 15 5, 12, 13 1, 12, 14 1, 8, 12

Explanation:

Step1: Check the triangle inequality theorem

For a set of three numbers \(a\), \(b\), \(c\) (\(a\leq b\leq c\)) to be the side - lengths of a triangle, the following must hold: \(a + b>c\).

For \(3,4,5\):

\(3 + 4=7>5\), \(3 + 5 = 8>4\), \(4+5=9>3\).

For \(9,12,15\):

\(9 + 12=21>15\), \(9 + 15=24>12\), \(12 + 15=27>9\).

For \(5,12,13\):

\(5+12 = 17>13\), \(5 + 13=18>12\), \(12+13=25>5\).

For \(1,12,14\):

\(1+12=13<14\).

For \(1,8,12\):

\(1 + 8=9<12\).

Step2: Check if they can form a right - triangle (since \(\angle B = 90^{\circ}\) in the given triangle, we can also use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (\(c\) is the hypotenuse))

For \(3,4,5\):

\(3^{2}+4^{2}=9 + 16=25=5^{2}\).

For \(9,12,15\):

\(9^{2}+12^{2}=81+144 = 225=15^{2}\).

For \(5,12,13\):

\(5^{2}+12^{2}=25 + 144=169=13^{2}\).

Answer:

A. \(3,4,5\), B. \(9,12,15\), C. \(5,12,13\)