Kate’s garden measures 15 yards by 12 yards. In order to make a path around it, she will need to reduce the size of her garden. The dimensions of the smaller garden will be related by a scale factor of 0.7.
What is the area of the path around the garden in square yards? Round your answer to the nearest square yard.
new dimensions:
.7(15) and .7(12)
new area = 10.5(8.4) = 88.2 yards^2
path = 15(12) - 88.2
=appr ......
Explanation
Area of current garden:
15 yd×12 yd=180 yd2
Dimensions of new garden scaled down by a factor of 0.7:
15yd×0.7=10.5yd12yd×0.7=8.4yd
Area of new garden:
10.5yd×8.4yd=88.2yd2
To find the area of the path find the difference between the current garden area and the new garden:
180yd2−88.2yd2=91.8yd2
Rounded to the nearest square yard, the area of the path is 92 yd².
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To find the area of the path around the garden, we first need to determine the area of the smaller garden that remains after reducing its size.
The scale factor of 0.7 tells us that the dimensions of the smaller garden will be 0.7 times the dimensions of the original garden. Therefore, we can find the dimensions of the smaller garden by multiplying the original dimensions by 0.7:
Length of smaller garden = 15 yards * 0.7 = 10.5 yards
Width of smaller garden = 12 yards * 0.7 = 8.4 yards
Now that we have the dimensions of the smaller garden, we can calculate its area:
Area of smaller garden = Length of smaller garden * Width of smaller garden
= 10.5 yards * 8.4 yards
= 88.2 square yards
Next, we need to find the area of the path around the garden. This can be done by subtracting the area of the smaller garden from the area of the original garden:
Area of path = Area of original garden - Area of smaller garden
= (15 yards * 12 yards) - 88.2 square yards
= 180 square yards - 88.2 square yards
= 91.8 square yards
To round our answer to the nearest square yard, we see that the decimal part is 0.8, which is greater than or equal to 0.5. Therefore, we round the answer up to the nearest whole number:
Area of path = 92 square yards
Therefore, the area of the path around the garden is approximately 92 square yards.