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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 tria…

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 tria…
asked 3.6k views
1 vote
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 hundredth?

asked
User Andy Mccullough
by
8.0k points

2 Answers

7 votes

Answer:

72.4 in.

Explanation:

answered
User Quake
by
8.2k points
6 votes
If the triangle were right-angled then the other 2 sides would be of length 30 / sqrt2 = 21.213 inches.

But it is acute angled so they will be a bit longer than this
they could be say 21.215 inches

So the required perimeter = 30 + 2*21.215 = 72.43 inches to nearest hundredth
answered
User Thomas Keller
by
8.0k points
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