Question

A rectangle is 4 times as long as it is wide. The perimeter of a rectangle is 50cm. Whatvis the length and width of the rectangle?Define the Variable & Write the Equations

Answer 1

Defining the variables:

`x\longrightarrow\text{ width}`

since the length is 4 times as long as the width

`4x\longrightarrow\text{length}`

Now, we use the formula for perimeter of a rectangle:

`\text{Perimeter}=2(WIDTH)+2(length)`

And we substitute the value of perimeter 50cm and the values defined for length and width:

`50=2(x)+2(4x)`

We solve this equation for x:

`\begin{gathered} 50=2x+8x \\ 50=10x \end{gathered}`

we divide both sides by 10:

`\begin{gathered} (50)/(10)=x \\ 5=x \end{gathered}`

We have the values of x.

Since we are asked for the length and width:

`\begin{gathered} \text{width}\longrightarrow x=5 \\ \text{length }\longrightarrow4x=4(5)=20 \end{gathered}`

Answer:

width: 5cm

length: 20cm