Question

The area of a rectangle is 45x^8y^9 square yards. If the length of the rectangle is 5x^3y^4 yards, which expression represents the width of the rectangle in yards?

Answer 1

`\bigstar` Area of a Rectangle is given by : Length × Width

Given : Area of the Rectangle = 45x⁸y⁹ square yards

Given : Length of the Rectangle = 5x³y⁴ square yards

Substituting the above values in the Area of the Rectangle formula,

We get :

`:\implies` 45x⁸y⁹ = (5x³y⁴) × Width

`:\implies \mathsf{Width = (45x^(8)y^(9))/(5x^(3)y^(4))}`

`:\implies \mathsf{Width = 9x^(5)y^(5)}`

Answer : Width of the Rectangle is 9x⁵y⁵ square yards

Answer 2

Explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

Therefore,

Width = Area/length

The area of the given rectangle is 45x^8y^9 square yards. If the length of the rectangle is 5x^3y^4 yards, then, an expression which represents the width of the rectangle in yards would be

W = 45x^8y^9/5x^3y^4

Applying rules of indices, it becomes

W = [45x^(8 - 3) × y^(9 - 4)]/5

W = 9x^5y^5 yards