Question

1. the area of a rectangle is $24w^{2}$ and has a width of $6w$. write an expression to represent the length.

$w = width$
$\frac{24w^{2}}{6w}$
use any strategy to solve these problems.

1. state the dimensions of two possible rectangles that could have an area of $4x^{2}+12cm^{2}$.
2. the area of a $16x^{2}cm^{2}$.

a. what is the leng the sides?
b. if the area is mult 100 how big are th side lengths?

Explanation:

Step1: Recall the formula for the area of a rectangle

The area formula of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. We need to solve for \(l\), so \(l=\frac{A}{w}\).

Step2: Substitute the given values into the formula

Given \(A = 24w^{2}\) and \(w = 6w\). Then \(l=\frac{24w^{2}}{6w}\).

Step3: Simplify the expression

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (\(a
eq0\)) and \(\frac{24}{6}=4\), \(\frac{w^{2}}{w}=w^{2-1}=w\). So \(l = 4w\).

Answer:

\(4w\)