For a constant area, the length of a rectangle varies inversely as its width. The length of a
rectangle is 27 ft when the width is 10 ft. Find the width of a rectangle with the same area if the
length is 18 ft.
LW = A
So, you want W such that
18W = 27*10
Area of a rectangle is to remain constant at 30cm then the width varies inversely as the length write a formula giving the width in terms of the length
To solve this problem, we can use the concept of inverse variation.
Let L be the length of the rectangle, W be the width of the rectangle, and A be the area of the rectangle.
We know that L varies inversely with W, so we can write the equation:
L ∝ 1/W
This can be rewritten as:
L = k/W (where k is the constant of variation)
We are given that the length L is 27 ft when the width W is 10 ft. We can substitute these values into the equation to find k:
27 = k/10
To solve for k, we can multiply both sides by 10:
270 = k
Now that we have the value of k, we can use it to find the width W when the length L is 18 ft:
18 = 270/W
To solve for W, we can cross-multiply and divide:
18W = 270
W = 270/18
W = 15
Therefore, the width of the rectangle with the same area, when the length is 18 ft, is 15 ft.
To solve this problem, we need to use the concept of inverse variation. In inverse variation, two variables are related in such a way that the product of the two variables remains constant.
Let's denote the length of the rectangle as L and the width of the rectangle as W. Since we are given that the area of the rectangle is constant, we can say that:
Area = Length * Width
Therefore, in this case, we can write:
Area = L * W
Now, given that the length varies inversely with the width, we can express this relationship as:
L = k/W
where k is the constant of variation.
To find the value of k, we can use the given information. When the length is 27 ft and the width is 10 ft, we can substitute these values into the equation above:
27 = k/10
To solve for k, we can multiply both sides of the equation by 10:
10 * 27 = k
270 = k
Now that we have the value of k, we can use it to find the width of the rectangle when the length is 18 ft. Substitute the values into the equation:
18 = 270/W
To solve for W, we can multiply both sides of the equation by W:
18W = 270
Divide both sides of the equation by 18:
W = 270/18
W = 15
Therefore, the width of the rectangle with the same area when the length is 18 ft is 15 ft.