Respuesta :
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
[tex]\text{Perimeter of a rectangle = 2(l + w)}[/tex]Where l is the length and w is the width of the rectangle
Recall, length = 3 times the width of the alley
Mathematically,
[tex]\begin{gathered} l\text{ = 3 }\times\text{ w} \\ l\text{ = 3w} \end{gathered}[/tex]Step 2: Substitute the value of l = 3w into the above formula
[tex]\begin{gathered} P\text{ = 2(l + w)} \\ p\text{ = 24m} \\ l\text{ = 3w} \\ 24\text{ = 2(3w + w)} \end{gathered}[/tex]Step 3: Solve for w
[tex]\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}[/tex]From the calculations above, you will see that the width of the playing alley is 3m
Step 4: Solve for l
[tex]\begin{gathered} \text{Recall, l = 3w} \\ w\text{ = 3} \\ l\text{ = 3 }\times3 \\ l\text{ = 9m} \end{gathered}[/tex]Hence, the length of the playing alley is 9m
