A rectangular quilt's length is twice the length of a rectangular picture, and the quilt's width is three times the width of the same picture. The area of the picture is 2 square feet. What is the area of the quilt, in square feet?
L w = 2
2 L * 3 w = 6*2 = 12
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Oh, I see. So the area of the picture is 2 square feet. That means we just need to find the area of the quilt. Let's do some math!
Since the length of the quilt is twice the length of the picture, that means the length of the quilt is 2 * 2 = 4 feet.
And since the width of the quilt is three times the width of the picture, that means the width of the quilt is 3 * 2 = 6 feet.
To find the area of the quilt, we just multiply the length by the width: 4 feet * 6 feet = 24 square feet.
So, the area of the quilt is 24 square feet. Voila!
To find the area of the quilt, we first need to determine the dimensions of the quilt.
Let's assume the length of the rectangular picture is x feet, and its width is y feet.
Since the length of the quilt is twice the length of the picture, the length of the quilt is 2x feet.
Similarly, the width of the quilt is three times the width of the picture, so the width of the quilt is 3y feet.
The area of the picture is given as 2 square feet, so the area of the picture is xy = 2 square feet.
Now we can find the area of the quilt by multiplying its length by its width:
Area of the quilt = length of the quilt × width of the quilt
= (2x feet) × (3y feet)
= 6xy square feet
Since we know that xy = 2 square feet, we can substitute this value into the equation:
Area of the quilt = 6xy square feet
= 6(2 square feet)
= 12 square feet
Therefore, the area of the quilt is 12 square feet.
To find the area of the quilt, we need to know the dimensions (length and width) of the quilt. Let's start by figuring out the dimensions of the picture.
The problem states that the area of the picture is 2 square feet. Since area is calculated by multiplying length and width, we can express this as a mathematical equation: length × width = area.
Let's say the length of the rectangular picture is L and the width is W. According to the problem, the area of the picture (2 square feet) is equal to L × W.
Now, the problem also states that the length of the quilt is twice the length of the picture. Therefore, the length of the quilt is 2L.
Similarly, the width of the quilt is three times the width of the picture, so the width of the quilt is 3W.
To find the area of the quilt, we need to calculate the product of its length and width. Therefore, the area of the quilt, Aq, can be expressed as: Aq = length of quilt × width of quilt.
Substituting in the values we found earlier, Aq = 2L × 3W.
Now, let's substitute L × W = 2 into the above equation: Aq = 2L × 3W = 2 × 2 × 3.
Multiplying 2 × 2 × 3 = 12, we find that the area of the quilt is 12 square feet.
Therefore, the area of the quilt is 12 square feet.