Answer:
The width = 38 yard
Step-by-step explanation:
Given
Dimension of Park = 32 by 24 yard
Area = 1748 yd²
Required
Find the width of the park
Given that the park is surrounded by a trail;
Let the distance between the park and the trail be represented with y;
Such that, the dimension of the park becomes (32 + y + y) by (24 + y + y) because it is surrounded on all sides
Area of rectangle is calculated as thus;
Area = Length * Width
Substitute 1748 for area; 32 + 2y and 24 + 2y for length and width
The formula becomes
Open Bracket
Subtract 1748 from both sides
Rearrange
Divide through by 4
Expand
Factorize
Split the above into two
But y can't be less than 0;
Recall that the dimension of the park is 32 + 2y by 24 + 2y
So, the dimension becomes 32 + 2*7 by 24 + 2*7
Dimension = 32 + 14 yard by 24 + 14 yard
Dimension = 46 yard by 38 yard
<em>Hence, the width = 38 yard</em>