Question

The area of a rectangle is 48x®y7

square yards. If the length of the
rectangle is 6x2y4 yards, which
expression represents the width of the
rectangle in yards?
A. 42x4y3
B. 42x6y3
C. 8x4y3
D. 8x6y3

Answer 1

To find the width of the rectangle with an area of 48x²y⁷ and a length of 6x²y⁴, divide the area by the length, resulting in a width of 8y³. We express this as width = 8y³ yards, which corresponds to option C.

Step-by-step explanation:

To solve for the width of the rectangle, we start with the given area formula for a rectangle, which is Area = length × width. From the information provided, the area of the rectangle is 48x²y⁷ square yards, and the length is 6x²y⁴ yards. Therefore, the width can be found by dividing the area by the length.

The formula to find the width will be:

• Width = Area / Length
• Width = 48x²y⁷ / 6x²y⁴
• Width = 8y³

Now, to express the width with x as well, we need just to rewrite it incorporating x:

• Width = 8x²y³×(x² / x²)

Since x²/x² equals 1, we can ignore this part in our final answer, and the width is simply 8y³ yards, which matches the option (C) 8x°y³.

Answer 2

D

Step-by-step explanation:

Remember, area equals width x height so you can set up this equation.

`48x^8y^7=6x^2y^4 * w`

Solving for w,

`(48x^8y^7)/(6x^2y^4) =w`

Simplifying,

`8x^6y^3`

Thus, D is the answer