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 in.
51.2 in.
72.4 in.
81.2 in.

The smallest perimeter is 72.44 inches. The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. As much as possible, the sum of the length of the two remaining side must be greater than the other side. Given the side is 30, then the sum of the two remaining sides should be greater than 30 inches.

The smallest possible perimeter of the triangle is 72.4 in.

A triangle is a three-sided polygon with three vertices and three angles. An acute triangle is a triangle in which the three angles are acute (less than 90 degrees).

The perimeter is the sum of the length of the three sides of the triangle.  Since the longest side measures 30 inches, the other sides must measure greater than 30 inches. Thus, the perimeter must exceed 60 inches.

To learn more about how a triangle, please check:

boxplot

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl