Defining the variables:
[tex]x\longrightarrow\text{ width}[/tex]since the length is 4 times as long as the width
[tex]4x\longrightarrow\text{length}[/tex]Now, we use the formula for perimeter of a rectangle:
[tex]\text{Perimeter}=2(WIDTH)+2(length)[/tex]And we substitute the value of perimeter 50cm and the values defined for length and width:
[tex]50=2(x)+2(4x)[/tex]We solve this equation for x:
[tex]\begin{gathered} 50=2x+8x \\ 50=10x \end{gathered}[/tex]we divide both sides by 10:
[tex]\begin{gathered} \frac{50}{10}=x \\ 5=x \end{gathered}[/tex]We have the values of x.
Since we are asked for the length and width:
[tex]\begin{gathered} \text{width}\longrightarrow x=5 \\ \text{length }\longrightarrow4x=4(5)=20 \end{gathered}[/tex]Answer:
width: 5cm
length: 20cm
