Question

Mr. Johnston currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 5 feet shorter than three times its width. He decides that the perimeter should be 70 feet. Determine the dimensions, in feet, of his new garden.

A. Length: 15 feet, Width: 10 feet
B. Length: 12 feet, Width: 9 feet
C. Length: 13 feet, Width: 8 feet
D. Length: 14 feet, Width: 9 feet

Answer 1

The correct dimensions for Mr. Johnston's new rectangular garden are a length of 25 feet and a width of 10 feet, based on the given perimeter of 70 feet. The options provided in the question do not include these dimensions, suggesting a discrepancy in the question or the answers provided.

Step-by-step explanation:

Let's take a systematic approach to solve Mr. Johnston's garden redesign. Given that the perimeter of the new rectangular garden is 70 feet and the length (L) is 5 feet shorter than three times the width (W), we can write two equations based on the properties of rectangles:

1. L = 3W - 5
2. The perimeter P of a rectangle is given by P = 2L + 2W, so 70 = 2(3W - 5) + 2W

We can solve for W in the second equation:

70 = 2(3W - 5) + 2W
70 = 6W - 10 + 2W
70 = 8W - 10
80 = 8W
W = 10

Now that we know the width, we can find the length:

L = 3(10) - 5 = 30 - 5 = 25

Thus, the dimensions of the new garden are:

• Length: 25 feet
• Width: 10 feet

The correct answer is not listed among the options provided, indicating a possible mistake in the question or the answer choices.