Statement Problem: Find the value of x in the diagram below, given the perimeter of a rectangle as 20centimeters.
Solution:
The perimeter of a rectangle is;
[tex]P=2(l+w)[/tex]
Where the length and width of the given rectangle is;
[tex]\begin{gathered} l=(x+3)cm \\ w=(x+1)cm \end{gathered}[/tex]
Thus, the value of x is;
[tex]\begin{gathered} 2(l+w)=20 \\ 2(x+3+x+1)=20 \\ \text{Divide both sides by 2},\text{ we have;} \\ \frac{2\mleft(x+3+x+1\mright)}{2}=\frac{20}{2} \\ x+3+x+1=10 \\ \text{Collect like terms, we have;} \\ 2x+4=10 \\ \end{gathered}[/tex]
Then, we subtract 4 from both sides of the equation, we have;
[tex]\begin{gathered} 2x+4-4=10-4 \\ 2x=6 \\ \text{Divide both sides by 2, we have;} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]
The value of x is 3
