The longest side of an acute triangle measures 30inches. The two remaining sides are congruent, but their length is unknown. Wha

Question

WINSTONCH [101]

3 years ago

12

The longest side of an acute triangle measures 30inches. The two remaining sides are congruent, but their length is unknown. Wha

t is the smallest possible perimeter of the triangle, rounded out the nearest hundredth

Mathematics

1 answer:

Nitella [24] · Answer 1 · 2022-01-10T15:28:21+03:00

The two short sides must be longer than those required in an isosceles right triangle. The ratio of side length to hypotenuse length in a 45°-45°-90° triangle is 1 : √2. So, such a triangle requires side lengths of 30/√2 ≈ 21.213 inches. Its perimeter will be about

... (30 +21.213 +21.213) in = 72.426 in

Since the perimeter needs to be slightly longer than that for the triangle to be acute, the smallest possible perimeter is ...

... 72.43 in