Question

the perimeter of the scalene triangle is 54.6 cm. which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8 + b = 54.6

Explanation:

Step1: Calculate the length of side \(3a\)

Given \(a = 8.7\) cm, then \(3a=3\times8.7 = 26.1\) cm.

Step2: Use the perimeter formula of a triangle

The perimeter \(P\) of a triangle is \(P=a + b+3a\). Substituting \(a = 8.7\) cm into \(a + 3a\), we get \(a+3a=8.7 + 26.1=34.8\) cm. Since \(P = 54.6\) cm, and \(P=(a + 3a)+b\), the equation becomes \(34.8 + b=54.6\).

Answer:

\(34.8 + b=54.6\) (the fourth option in the multiple - choice list)