Question 6

We will use a variable to represent the unknown lengths and form an equation.

Step 1 — Define variables and form the equation

Let's say the shorter piece is $x$ feet long.

The longer piece is four times the shorter piece.

So, the longer piece is $4x$ feet long.

The total length of the fence is 300 feet.

We add the lengths of the two pieces to get the total.

$x + 4x = 300$

$5x = 300$

$\boxed{5x = 300}$

Step 2 — Find the length of the shorter piece

Now, we need to solve for $x$.

We divide both sides of the equation by 5.

$x = \frac{300}{5}$

$x = 60$

$\boxed{x = 60 \text{ feet}}$

Step 3 — Find the length of the longer piece

The longer piece is $4x$.

We substitute the value of $x$ we found.

$4 \times 60$

$= 240$

$\boxed{240 \text{ feet}}$

Answer

(i) The shorter piece is 60 feet long. (ii) The longer piece is 240 feet long.