the perimeter of this hexagon is 162 cm. each longer side measures 1cm more than twice a shorter side. find the length of the side labeled x.
20
To find the length of the side labeled x, we need to analyze the given information about the hexagon's perimeter. Let's break down the problem into steps:
Step 1: Determine the number of sides in the hexagon
A hexagon has six sides, so the perimeter is the sum of all the sides.
Step 2: Set up equations for the sides
Let's assume that the shorter side of the hexagon measures x cm. According to the information given, each longer side is 1 cm more than twice the shorter side.
Therefore, the equation for the length of the longer side is: 2x + 1.
Step 3: Write the equation for the perimeter
Since the perimeter of the hexagon is given as 162 cm, we can write the equation:
Perimeter = Sum of all the sides
162 cm = x + (2x + 1) + (2x + 1) + (2x + 1) + (2x + 1) + (2x + 1)
Now, simplify the equation:
162 cm = x + 2x + 1 + 2x + 1 + 2x + 1 + 2x + 1 + 2x + 1
162 cm = 11x + 6
Step 4: Solve the equation
To solve the equation for x, isolate the x-term by subtracting 6 from both sides:
162 cm - 6 = 11x
156 cm = 11x
Next, divide both sides by 11 to solve for x:
x = 156 cm ÷ 11
x = 14 cm
Therefore, the length of the side labeled x is 14 cm.
By following these steps, we determined that the length of the side labeled x is 14 cm.
side1 = x
side2 = 2x+1
side3 = 2(2x+1) + 1 = 4x + 3
side4 = 2(4x+3) + 1 = 8x + 7
side5 = 2(8x+7) + 1 = 16x + 15
side5 = 32x + 31
add them up = 162
solve for x