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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
5. The Triangle Inequality
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Exercise 4 Page 448

Use the Triangle Inequality Theorem.

B

Practice makes perfect

We are given the lengths of two of the triangle's sides, 5 yards and 9 yards. We will use the Triangle Inequality Theorem to figure out which of the given options is the least possible measurement of the third side. Let's find the sums of the side lengths to see if they meet the requirements for the Triangle Inequality Theorem.

Option Side Lengths Sums
A 4, 5, and 9 yards 4 + 5 & = 9 & * 4 + 9 & > 5 & ✓ 5 + 9 & > 4 & ✓
B 5, 5, and 9 yards 5 + 5 & > 9 & ✓ 5 + 9 & > 5 & ✓ 5 + 9 & > 5 & ✓
C 6, 5, and 9 yards 6 + 5 & > 9 & ✓ 6 + 9 & > 5 & ✓ 5 + 9 & > 6 & ✓
D 14, 5, and 9 yards 14 + 5 & > 9 & ✓ 14 + 9 & > 5 & ✓ 5 + 9 & = 14 & *

Both 5 yards and 6 yards would satisfy the theorem but 5 is the lesser number so B is the correct answer.

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