Question

The remains of an ancient ball court include a rectangular playing alley with a perimeter of about 24m. The length of the alley is three times the width. Find the length and the width of the playing alley.The width is ? m and the length is ? m

Answer 1

ANSWER

Length of the playing alley = 9m

Width of the playing alley = 3m

STEP-BY-STEP EXPLANATION:

Given information

The perimeter of a rectangular playing alley = 24 m

The length of the alley is three times the width

Let l represents the length of the alley

Let w represents the width of the alley

Step 1: Write the formula for calculating the perimeter of a rectangle

$\text{Perimeter of a rectangle = 2(l + w)}$

Where l is the length and w is the width of the rectangle

Recall, length = 3 times the width of the alley

Mathematically,

$\begin{gathered} l\text{ = 3 }\times\text{ w} \\ l\text{ = 3w} \end{gathered}$

Step 2: Substitute the value of l = 3w into the above formula

$\begin{gathered} P\text{ = 2(l + w)} \\ p\text{ = 24m} \\ l\text{ = 3w} \\ 24\text{ = 2(3w + w)} \end{gathered}$

Step 3: Solve for w

$\begin{gathered} 24\text{ = 2(4w)} \\ 24\text{ = 8w} \\ \text{Divide both sides by 8} \\ \frac{24}{8}\text{ = }\frac{8w}{8} \\ w\text{ = 3 m} \end{gathered}$

From the calculations above, you will see that the width of the playing alley is 3m

Step 4: Solve for l

$\begin{gathered} \text{Recall, l = 3w} \\ w\text{ = 3} \\ l\text{ = 3 }\times3 \\ l\text{ = 9m} \end{gathered}$

Hence, the length of the playing alley is 9m