Final answer:
To find the length of the rectangular park, we first solve for the variable x using the perimeter formula and then substitute back into the length expression, resulting in a length of 17 meters.
Step-by-step explanation:
The student is asking for the length of the rectangular park with a given perimeter and expressions for length and width in terms of a variable x. We know that the perimeter (P) of a rectangle is given by P = 2l + 2w, where 'l' is the length and 'w' is the width. In this case, we are given P = 90, l = 4x + 1, and w = 6x + 4.
To solve for the length, we first need to substitute the expressions for length and width into the formula for the perimeter:
90 = 2(4x + 1) + 2(6x + 4)
This simplifies to:
90 = 8x + 2 + 12x + 8
90 = 20x + 10
Then, we subtract 10 from both sides and solve for x:
80 = 20x
x = 4
Now that we have the value of x, we can determine the length of the rectangular park by substituting x back into the expression for length:
l = 4x + 1 = 4(4) + 1 = 17
Therefore, the length of the rectangular park is 17 meters.