Question

compare the given dimensions of four triangles. which triangle is possible to construct?
side lengths of 2 ft, 11 ft,
and 15 ft
side lengths of 4 ft, 8 ft,
and 15 ft
side lengths of 3 ft, 7 ft,
and 11 ft
side lengths of 5 ft, 12 ft,
and 13 ft

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

For side lengths \(2\) ft, \(11\) ft, and \(15\) ft:

\(2+11 = 13<15\). So, this is not a valid triangle.

For side lengths \(4\) ft, \(8\) ft, and \(15\) ft:

\(4 + 8=12<15\). So, this is not a valid triangle.

For side lengths \(3\) ft, \(7\) ft, and \(11\) ft:

\(3+7 = 10<11\). So, this is not a valid triangle.

For side lengths \(5\) ft, \(12\) ft, and \(13\) ft:

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

Answer:

The triangle with side lengths of \(5\) ft, \(12\) ft, and \(13\) ft is possible to construct.