An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.
A) 2.9 ft
B) 1.3 ft
C) 6.2 ft
D) 5.1 ft
E) 1.8 ft

Question

Quizplus · Accepted Answer

The area of an equilateral triangle is given by the formula $A = \frac{\sqrt{3}}{4}a^2$, where $a$ is the length of a side. Rearranging to solve for $a$, we get $a = \sqrt{\frac{4A}{\sqrt{3}}}$. Substituting $A = 3.6$ square feet, we find $a \approx 2.9$ feet.

An Unusual Architectural Design Requires Triangular Ducts That Will Be