Question

bell work alg 1 adan ismael torres 1). 09/12 the perimeter of a triangle is 13in. what length (inches) is the shortest side x - 5in $\frac{x}{2}$in (a + b = c) 6

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. So, $x+(x - 5)+\frac{x}{2}=131$.

Step2: Combine like - terms

First, combine the $x$ terms: $x+x+\frac{x}{2}-5 = 131$. Then, $2x+\frac{x}{2}=131 + 5$. The common denominator for the $x$ terms is 2, so $\frac{4x}{2}+\frac{x}{2}=136$, which simplifies to $\frac{4x + x}{2}=136$, or $\frac{5x}{2}=136$.

Step3: Solve for $x$

Multiply both sides of the equation $\frac{5x}{2}=136$ by $\frac{2}{5}$: $x=\frac{136\times2}{5}=\frac{272}{5}=54.4$.

Step4: Find the side - lengths

The side - lengths are:

• First side: $x=54.4$ inches.
• Second side: $x - 5=54.4-5 = 49.4$ inches.
• Third side: $\frac{x}{2}=\frac{54.4}{2}=27.2$ inches.

Answer:

27.2 inches