The area if a rectangle is x3y4. Which expression represents the length if the width is x2y
To find the length of the rectangle, we can use the formula for the area of a rectangle:
Area = Length × Width
In this case, the area is given as x^3y^4, and the width is x^2y.
So we can set up the equation:
x^3y^4 = Length(x^2y)
To find the length, we need to isolate it on one side of the equation.
Divide both sides of the equation by (x^2y):
x^3y^4 / (x^2y) = Length(x^2y) / (x^2y)
Simplifying:
xy^3 = Length
Therefore, the expression that represents the length is xy^3.
To find the length of the rectangle, we can use the formula for the area of a rectangle:
Area = Length × Width
Given that the area of the rectangle is x^3y^4, and the width is x^2y, we can substitute these values into the formula:
x^3y^4 = Length × x^2y
To solve for the length, we divide both sides of the equation by x^2y:
Length = x^3y^4 / (x^2y)
Simplifying this expression, we subtract the exponents of x (3 - 2) and y (4 - 1):
Length = x^(3-2)y^(4-1)
Length = x^1y^3
Therefore, the expression that represents the length of the rectangle, given the width x^2y, is x^1y^3, which simplifies to xy^3.
Since A = WL, L=A/W
x^3y^4 / x^2y = xy^3