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. use the distributive property to simplify the equation.
( a+\frac{1}{2}a+a + 1=\frac{1}{3}(a + 42) )
( a+\frac{1}{2}a+a + 1=square a+square )

Explanation:

Step1: Aplicar la propiedad distributiva

La propiedad distributiva \(c(a + b)=ca+cb\). Aquí \(c = \frac{1}{3}\), \(a=a\) y \(b = 42\). Entonces \(\frac{1}{3}(a + 42)=\frac{1}{3}a+\frac{1}{3}\times42\).

Step2: Calcular \(\frac{1}{3}\times42\)

\(\frac{1}{3}\times42 = 14\).

Answer:

\(a+\frac{1}{2}a + a+1=\frac{1}{3}a + 14\)