Question

Emily knows that the area of a rectangle is 54x9y8 square yards and that it’s length 6x3y4 yards. If she divides the area by the length to find the width, then which expression represents the width of her rectangle in yards?

A 9x3y2 B 48x6y4 C 9x6y4 D 60x12y12

Answer 1

Width of the rectangle is:
`\mathbf{Width= 9x^6 y^4}`

Option C is correct.

Explanation:

Area of rectangle =
`54x^9y^8`

Length of rectangle =
`6x ^ 3y^4`

We need to find width of rectangle.

The formula used is:

`Area\:of\:rectangle=Length* Width\\Width=(Area\:of\:rectangle)/(Length)`

Putting values in the formula to find Width of rectangle

`Width=(Area\:of\:rectangle)/(Length)\\Width=(54x^9y^8)/(6x^ 3y^4)`

Using the exponent rule:
`(a^m)/(a^n)=a^(m-n)`

and simplifying the terms we get

`Width=(54x^9y^8)/(6x^3y^4)\\Width=9x^(9-3) \: y^(8-4)\\Width=9x^6 y^(4)`

So, Width of the rectangle is:
`\mathbf{Width= 9x^6 y^4}`

Option C is correct.