P = 2(L + W) The preceding formula gives the perimeter P of a rectangle with length L and width W. An outdoor patio is in the shape of a rectangle and has a perimeter of 48 feet. The width of the patio is 4 feet less than the length of the patio. What is the width, in feet, of the patio?

Rationale

The width of the patio is 10 feet.

To find the width of the patio, we can set up the equations based on the information provided. Given that the width is 4 feet less than the length and the perimeter is 48 feet, we can solve for the dimensions of the patio.

A (10) CORRECT

If we let the length be L, then the width is L - 4. The perimeter formula gives us: P = 2(L + W) = 2(L + (L - 4)) = 2(2L - 4) = 48. Solving this, we find L = 14, and thus the width W = 14 - 4 = 10 feet, confirming this choice is correct.

B (12) YOUR ANSWER

If the width were 12 feet, then the length would be 12 + 4 = 16 feet. Using the perimeter formula: P = 2(16 + 12) = 2(28) = 56 feet, which does not match the given perimeter of 48 feet. Therefore, this option is incorrect.

C (20) YOUR ANSWER

Assuming the width is 20 feet, the length would be 20 + 4 = 24 feet. The perimeter would then be P = 2(20 + 24) = 2(44) = 88 feet, which is significantly larger than the required 48 feet. Hence, this choice is also incorrect.

D (24) YOUR ANSWER

If the width were 24 feet, the length would be 24 + 4 = 28 feet. Plugging these values into the perimeter formula gives: P = 2(24 + 28) = 2(52) = 104 feet, which again exceeds the perimeter of 48 feet. Thus, this option is incorrect as well.

Conclusion

In solving the problem, we determined that the only viable solution for the width of the patio, given the conditions of the perimeter and the relationship between length and width, is 10 feet. This highlights the importance of correctly applying the perimeter formula and understanding the relationship between the dimensions of a rectangle.

P = 2(L + W) The preceding formula gives the perimeter P of a rectangle with length L and width W. An outdoor patio is in the shape of a rectangle and has a perimeter of 48 feet. The width of the patio is 4 feet less than the length of the patio. What is the width, in feet, of the patio?

The width of the patio is 10 feet.

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