Question

the areas of the rectangles are given. factor out the gcf to find expressions for the missing dimensions.

the width is $square$. the length of the first rectangle is $square$, and the length of the second rectangle is $square$.
(simplify your answers.)

Explanation:

Step1: Find GCF of terms

First, factor each term:
$25xy^2 = 5^2 \cdot x \cdot y^2$
$30x^2y^4 = 2 \cdot 3 \cdot 5 \cdot x^2 \cdot y^4$
The GCF is $5xy^2$.

Step2: Factor first rectangle area

Divide $25xy^2$ by GCF to find length:
$\frac{25xy^2}{5xy^2} = 5$

Step3: Factor second rectangle area

Divide $30x^2y^4$ by GCF to find length:
$\frac{30x^2y^4}{5xy^2} = 6xy^2$

Answer:

The width is $5xy^2$. The length of the first rectangle is $5$, and the length of the second rectangle is $6xy^2$.