Question

a rectangle has an area of \\(50x^5y^5\\) and a length of \\(25x^3y\\). which of the following represents the width of the rectangle?

a. \\(2x^2y^4\\)
b. \\(25x^2y^4\\)
c. \\(25x^8y^6\\)
d. \\(2x^8y^6\\)

Explanation:

Relate area, length, and width

Using the Geometric Formulas knowledge point

$$ \text{Area} = \text{length} \times \text{width} \implies \text{width} = \frac{\text{Area}}{\text{length}} $$

Substitute the given expressions

Using the Algebraic Simplification knowledge point

$$ \text{width} = \frac{50x^5y^5}{25x^3y} $$

Simplify the coefficients

Using the Algebraic Simplification knowledge point

$$ \frac{50}{25} = 2 $$

Apply exponent rules to simplify variables

Using the Exponent Rules knowledge point

$$
LATEXBLOCK0
$$

Combine the simplified terms

Using the Algebraic Simplification knowledge point

$$ \text{width} = 2x^2y^4 $$

Answer:

• (A) \(2x^2y^4\) (Correct answer)
• (B) \(25x^2y^4\)
• (C) \(25x^8y^6\)
• (D) \(2x^8y^6\)