Question

1. geometry the perimeter of a triangle is 56 cm. sides #1 and #2 have equal length, while side #3 is four centimeters shorter than side #1. write and solve an equation to determine the length of side 1. use the variable x = length of side 1 to write your equation. show your work.

Explanation:

Step1: Set up the equation

Let the length of side #1 and side #2 be \(x\) cm. The perimeter of a triangle is the sum of all its sides. So, \(x + x+4 = 56\).

Step2: Simplify the equation

Combine like - terms: \(2x+4 = 56\).

Step3: Isolate the variable term

Subtract 4 from both sides: \(2x+4 - 4=56 - 4\), which gives \(2x = 52\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{52}{2}\).

Answer:

The length of side #1 is \(26\) cm.