The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.
What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?
$41.0 \mathrm{in}$
51.2 in.
72.4 in.
81.2 in.
Answer
Round the perimeter to the nearest tenth: \(\boxed{60.0}\) inches
Step 1 ：Given the longest side of an acute triangle measures 30 inches, and the two remaining sides are congruent with unknown length x.
Step 2 ：Using the triangle inequality theorem, we have: \(x + x > 30\) or \(2x > 30\)
Step 3 ：Solving for x, we get: \(x > 15\)
Step 4 ：Choose the smallest possible value for x just above 15 inches: \(x = 15.0000000001\)
Step 5 ：Calculate the perimeter: \(perimeter = 30 + 2x = 60.0000000002\)
Step 6 ：Round the perimeter to the nearest tenth: \(\boxed{60.0}\) inches
