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A rectangular park has a perimeter of 90 . The length is 4x + 1 and the width is 6x + 4. How long is the length?

User Stockton
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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.

User Louis Van Tonder
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