Question

question 15 (1 point) (01.06 mc) jason has 144 feet of material to build a fence around a rectangular garden on his property. if the width of the fence must be 9 feet, what is the length of the fence in yards if he uses all 144 feet of material?

a 126 yards

b 63 yards

c 42 yards

d 21 yards

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width. We know the perimeter \( P = 144 \) feet and the width \( w = 9 \) feet. We need to find the length \( l \) first in feet and then convert it to yards.

Step2: Solve for the length in feet

Substitute the known values into the perimeter formula:
\[
144 = 2(l + 9)
\]
Divide both sides by 2:
\[
\frac{144}{2}=l + 9
\]
\[
72=l + 9
\]
Subtract 9 from both sides:
\[
l=72 - 9
\]
\[
l = 63 \text{ feet}
\]

Step3: Convert feet to yards

Since 1 yard = 3 feet, to convert feet to yards, we divide the length in feet by 3:
\[
\text{Length in yards}=\frac{63}{3}=21 \text{ yards}
\]
Wait, no, wait. Wait, the question is asking for the length of the fence in yards. Wait, no, wait, let's re - check. Wait, the perimeter is 144 feet, width is 9 feet. Wait, maybe I made a mistake. Wait, no, the perimeter of the rectangle is \( P = 2(l + w) \). So \( 144=2(l + 9) \), so \( l + 9 = 72 \), so \( l=63 \) feet. But 63 feet is how many yards? Since 1 yard = 3 feet, \( 63\div3 = 21 \) yards? Wait, no, the options are 126, 63, 42, 21. Wait, maybe I misread the question. Wait, the question says "what is the length of the fence in yards". Wait, no, the perimeter is 144 feet, which is the total length of the fence. Wait, no, the fence is around the rectangular garden, so the perimeter is the length of the fence. Wait, no, the question is: Jason has 144 feet of material to build a fence (so perimeter \( P = 144 \) feet) around a rectangular garden. Width \( w = 9 \) feet. Find the length of the fence in yards? Wait, no, maybe the question is find the length (of the rectangle) in yards? Wait, no, let's re - examine the problem.

Wait, the problem says: "what is the length of the fence in yards if he uses all 144 feet of material?". Wait, no, the fence is the perimeter, so the length of the fence is 144 feet, but we need to find it in yards? Wait, no, 144 feet to yards: \( 144\div3 = 48 \) yards, but that's not an option. Wait, maybe the question is find the length of the rectangle (one of the sides) in yards. Let's re - do the steps.

Perimeter of rectangle \( P = 2(l + w) \), \( P = 144 \) feet, \( w = 9 \) feet.

So, \( 144=2(l + 9) \)

Divide both sides by 2: \( 72=l + 9 \)

Subtract 9: \( l = 63 \) feet. Now convert 63 feet to yards: \( 63\div3 = 21 \) yards? But 21 is an option (option d). Wait, but let's check again. Wait, maybe I messed up the formula. Wait, perimeter is \( 2l+2w \). So \( 2l + 2\times9=144 \), \( 2l+18 = 144 \), \( 2l=144 - 18=126 \), \( l = 63 \) feet. 63 feet is 21 yards (since 1 yard = 3 feet, 63/3 = 21). So the length of the rectangle (the side) is 63 feet, which is 21 yards. But the options are: a)126 yards, b)63 yards, c)42 yards, d)21 yards. So the answer is d)21 yards. Wait, but let's confirm the unit conversion. 1 yard = 3 feet, so to convert feet to yards, divide by 3. 63 feet divided by 3 is 21 yards. So the length of the fence's side (the length of the rectangle) is 21 yards.

Answer:

d. 21 yards