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madam [21]
2 years ago
5

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
Mathematics
1 answer:
Furkat [3]2 years ago
6 0

Answer:

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

Option C is correct.

Step-by-step 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\times Width\\Width=\frac{Area\:of\:rectangle}{Length}

Putting values in the formula to find Width of rectangle

Width=\frac{Area\:of\:rectangle}{Length}\\Width=\frac{54x^9y^8}{6x^ 3y^4}

Using the exponent rule: \frac{a^m}{a^n}=a^{m-n}

and simplifying the terms we get

Width=\frac{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.

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Since both equations give the same line, the first one has infinite solutions.

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