Question

can a triangle have sides with the given lengths? explain.
a = 2 yd, b = 3 yd, c = 4 yd

choose the correct statement below.
o a. yes because the sum of the lengths of any two sides is greater than the length of the third side, and this satisfies the triangle inequality theorem.
o b. no because the sum of the lengths of the two shorter sides is greater than the length of the third side, and this contradicts the triangle inequality th
o c. yes because the sum of the lengths of any two sides is less than the length of the third side, and this satisfies the triangle inequality theorem.
o d. no because the sum of the lengths of the two shorter sides is less than the length of the third side, and this contradicts the triangle inequality theor

Explanation:

Step1: Check sum of \(a + b\) and \(c\)

\(a + b=2 + 3=5\) yd. Since \(5>4\) (i.e., \(a + b>c\))

Step2: Check sum of \(a + c\) and \(b\)

\(a + c=2+4 = 6\) yd. Since \(6>3\) (i.e., \(a + c>b\))

Step3: Check sum of \(b + c\) and \(a\)

\(b + c=3 + 4=7\) yd. Since \(7>2\) (i.e., \(b + c>a\))

Answer:

A. Yes because the sum of the lengths of any two sides is greater than the length of the third side, and this satisfies the triangle inequality theorem.