Answer:
x = 2
Step-by-step explanation:
1. The perimeter is the distance around a 2D shape, meaning to find the perimeter we have to add: 2x + 2 + 2x + 2 + 4x + 3 + 4x + 3. Or, we could write it as 2(2x+2) + 2(4x+3).
2. Since we're already given the perimeter, 34, we can set up an equation of: [tex]2(2x+2) + 2(4x+3) = 34[/tex]
3. (Solving)
Step 1: Simplify both sides of the equation.
- [tex](2)(2x)+(2)(2)+(2)(4x)+(2)(3) = 34[/tex]
- [tex]4x + 4 + 8x + 6 = 34[/tex]
- [tex](4x+8x) + (4+6) = 34[/tex]
- [tex]12x + 10 = 34[/tex]
Step 2: Subtract 10 from both sides.
- [tex]12x + 10 - 10 = 34 - 10[/tex]
- [tex]12x = 24[/tex]
Step 3: Divide both sides by 12.
- [tex]\frac{12x}{12} = \frac{24}{12}[/tex]
- [tex]x = 2[/tex]
4. To check if our answer correct, let's plug in the value of x into our equation!
- [tex]2(2*2+2) + 2(4*2+3)=34[/tex]
- [tex]2(4+2) + 2(8+3) = 34[/tex]
- [tex]2(6) + 2(11) = 34[/tex]
- [tex]12 + 22 = 34[/tex]
- [tex]34 = 34[/tex]
Therefore, x = 2! I hope this helped you.
