Question

a triangle has side lengths $a$, $\frac{1}{2}a$, and $a + 1$ inches. the perimeter is equal to $\frac{1}{3}(a + 42)$ inches. solve the equation to find the side lengths and perimeter of the triangle. $a = 6$ list the side lengths of the triangle in order from shortest to longest. in., 6 in., in.

Explanation:

Step1: Calcular el valor de \(\frac{1}{2}a\)

Sustituir \(a = 6\) en \(\frac{1}{2}a\), \(\frac{1}{2}\times6=3\)

Step2: Calcular el valor de \(a + 1\)

Sustituir \(a = 6\) en \(a + 1\), \(6+1 = 7\)

Step3: Ordenar los lados

Comparar los valores \(3\), \(6\) y \(7\). \(3<6<7\)

Answer:

3 in., 6 in., 7 in.