A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Do these quantities vary directly or inversely?
The area of a rectangle is given by the formula length times width. In this case, the area of the first rectangle is 72 cm times 56 cm, which equals 4032 cm². The area of the second rectangle is also 4032 cm², but its width is 21 cm. Since the area remains the same while the width changes, these quantities vary inversely.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Find the constant of variation.
To find the constant of variation, you need to compare the length and width of the two rectangles.
The first rectangle has a length of 72 cm and a width of 56 cm. The second rectangle has the same area but a different width of 21 cm.
Let's denote the constant of variation as k. Since the two rectangles have the same area, we can set up the following equation:
72 cm * 56 cm = k * 21 cm
Simplifying the equation, we get:
4032 cm² = 21k cm
Dividing both sides by 21 cm, we have:
k = 4032 cm² / 21 cm
k ≈ 192 cm
Therefore, the constant of variation is approximately 192 cm.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. Find the constant of variation. If x and y vary inversely, then x·y is constant.
You are correct. Since the area of a rectangle is equal to the product of its length and width, the product of the length and width of both rectangles will be constant if they have the same area.
For the first rectangle with length 72 cm and width 56 cm, the product is:
72 cm * 56 cm = 4032 cm²
For the second rectangle with width 21 cm and an unknown length, the product is also:
21 cm * length = 4032 cm²
From this, we can find the length of the second rectangle:
length = 4032 cm² / 21 cm
length ≈ 192 cm
Therefore, the constant of variation between the length and width is approximately 192 cm.
No!
Apologies for the mistake in my previous response. Let's solve the problem correctly:
Given that the first rectangle has a length of 72 cm and a width of 56 cm, and the second rectangle has the same area, but its width is 21 cm.
The formula for the area of a rectangle is length times width.
For the first rectangle, the area is:
A1 = 72 cm * 56 cm = 4032 cm²
For the second rectangle, the width is 21 cm and the area is also 4032 cm². Let's denote the length of the second rectangle as L2.
So, the area of the second rectangle is:
A2 = L2 * 21 cm = 4032 cm²
To find the constant of variation, we can set up the following equation:
A1 = A2
4032 cm² = L2 * 21 cm
Now, we can solve for L2:
L2 = 4032 cm² / 21 cm
L2 ≈ 192 cm
Therefore, the constant of variation between the length and width is approximately 192 cm.
A rectangle has length 72 cm and width 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. What iis the length if the second rectangle?
To find the length of the second rectangle, we use the formula for the area of a rectangle, which is length times width.
The first rectangle has a length of 72 cm and a width of 56 cm, so its area is:
Area1 = 72 cm * 56 cm = 4032 cm²
The second rectangle has the same area but a width of 21 cm. Let's denote the length of the second rectangle as L.
The area of the second rectangle is:
Area2 = L * 21 cm
Since the two rectangles have the same area, we can set up the equation:
4032 cm² = L * 21 cm
To find the length of the second rectangle, we divide both sides of the equation by 21 cm:
L = 4032 cm² / 21 cm
L ≈ 192 cm
Therefore, the length of the second rectangle is approximately 192 cm.