Ms. Richardson is going to make a concrete path that will go along three sides of a rectangular lawn.
She has enough concrete for 175 square feet. She wants to find the width, in feet, of the path that would use all of the concrete.
To the nearest hundredth of a foot, what will be the width of the path?
A.
1.96 feet
B.
3.60 feet
C.
4.30 feet
D.
7.20 feet
We can use the formula for the area of the path to determine the width. Let x be the width of the path, and let the length and width of the lawn be L and W, respectively. The length of the path is L + W + L = 2L + W.
The area of the path is the difference between the area of the larger rectangle and the area of the smaller rectangle. We can express the area of the path as A = (L + 2x)(W + x) - L * W. We are given that A = 175 square feet.
Expanding and simplifying the equation for the area of the path gives 175 = 2Lx + Wx + x^2. We want to find the value of x that satisfies this equation. Since we don't have the values for L and W, we can't directly solve for x. However, we can try each of the given answer choices and see which one works.
A. x = 1.96 feet
Plugging this value into the equation gives 175 = 2L(1.96) + W(1.96) + (1.96)^2. Simplifying gives 175 = 3.92L + 1.96W + 3.8416. We can't determine the values of L and W, so we can't determine if this equation is true, so we need to try another answer choice.
B. x = 3.60 feet
Plugging this value into the equation gives 175 = 2L(3.60) + W(3.60) + (3.60)^2. Simplifying gives 175 = 7.2L + 3.6W + 12.96. We can't determine the values of L and W, so we can't determine if this equation is true, so we need to try another answer choice.
C. x = 4.30 feet
Plugging this value into the equation gives 175 = 2L(4.30) + W(4.30) + (4.30)^2. Simplifying gives 175 = 8.6L + 4.3W + 18.49. We can't determine the values of L and W, so we can't determine if this equation is true, so we need to try another answer choice.
D. x = 7.20 feet
Plugging this value into the equation gives 175 = 2L(7.20) + W(7.20) + (7.20)^2. Simplifying gives 175 = 14.4L + 7.2W + 51.84. This equation seems to involve larger numbers for L and W, which seems more reasonable for a 175 square foot path. Checking the other equations again, we notice that answer choice B also gives similar sized values for L and W. Since we are asked to find the width to the nearest hundredth of a foot, we can conclude that the width of the path is most likely closer to either 3.60 feet or 7.20 feet. Given the dimensions of a rectangular path, a width of 7.20 feet seems too large, so the width of the path is most likely around 3.60 feet.
Thus, the answer is B. 3.60 feet.