Question

The width of a rectangular garden is 2 feet more than one third of its length. The perimeter is 52 feet. Find the dimensions of the rectangle by writing an equation and solving.

A) Length = 12 feet, Width = 6 feet
B) Length = 8 feet, Width = 16 feet
C) Length = 10 feet, Width = 12 feet
D) Length = 6 feet, Width = 10 feet

Answer 1

To find the dimensions of the rectangle, set up an equation based on the perimeter and the relation between the width and length. Solve for the length first, then the width, finding that the correct dimensions are 12 feet in length and 6 feet in width, corresponding to option C.So, the correct option is: B) Length = 12 feet, Width = 8 feet

Step-by-step explanation:

The question involves solving for the dimensions of a rectangle given its perimeter and a relationship between its length and width. Represent the length as L and the width as W. The width is given as two feet more than one third of the length; W = \(\frac{1}{3}L + 2\). The perimeter (P) of a rectangle is P = 2L + 2W. Given P = 52 feet, you can substitute the expression for W into the perimeter equation to find L.

Perimeter equation: 52 = 2L + 2(\(\frac{1}{3}L + 2\))

Solve for L, then use L to find W. After solving, the correct dimensions corresponding to option C are revealed: Length = 12 feet, Width = 6 feet.So, the correct option is: B) Length = 12 feet, Width = 8 feet

Answer 2

By applying algebraic expressions to the given problem, we find that the length of the rectangular garden is 18 feet, and the width is 8 feet. None of the options provided (A, B, C, D) match this result, indicating a discrepancy.

Step-by-step explanation:

The student is asked to find the dimensions of a rectangular garden where the width is 2 feet more than one third of its length and the perimeter is 52 feet. To express this mathematically:

• Let the length be L feet.
• Then the width W is given as W = L/3 + 2 feet.

The perimeter P of a rectangle is given by P = 2L + 2W. Using the given perimeter of 52 feet:

1. P = 2L + 2W = 52
2. Substitute the expression for W into the perimeter equation:
3. 52 = 2L + 2(L/3 + 2)
4. Simplify and solve for L:
5. 52 = 2L + 2/3L + 4
6. 48 = 8/3L
7. L = 18
8. Now, calculate W:
9. W = 18/3 + 2 = 6 + 2 = 8

Therefore, the dimensions of the rectangle are Length = 18 feet and Width = 8 feet. However, none of the options given match this result, indicating a possible mistake in the given options or a misinterpretation of the question.