Question

the street sign shown is a regular hexagon with side lengths of (7.6x + 10.4) centimeters. the perimeter of the sign is 737.28 centimeters. write and solve an equation to find the side length of the street sign. answer: ______ cm (enter numerical value, rounded to the nearest tenth)

Explanation:

Step1: Set up the perimeter - equation

A regular hexagon has 6 equal - length sides. If the length of each side is \(7.6x + 10.4\) and the perimeter \(P\) is 737.28, then the equation for the perimeter is \(P=6(7.6x + 10.4)\). So, \(6(7.6x + 10.4)=737.28\).

Step2: Distribute the 6

Using the distributive property \(a(b + c)=ab+ac\), we have \(6\times7.6x+6\times10.4 = 737.28\), which simplifies to \(45.6x+62.4 = 737.28\).

Step3: Isolate the variable term

Subtract 62.4 from both sides of the equation: \(45.6x+62.4 - 62.4=737.28 - 62.4\), resulting in \(45.6x=674.88\).

Step4: Solve for \(x\)

Divide both sides of the equation by 45.6: \(x=\frac{674.88}{45.6}=14.8\).

Step5: Find the side - length

Substitute \(x = 14.8\) into the side - length formula \(7.6x + 10.4\). So, \(7.6\times14.8+10.4=112.48+10.4 = 122.9\) (rounded to the nearest tenth).

Answer:

122.9