Question

1. if you increase the length of a rectangle, then the area will ___. *

o increase
decrease
o remain the same

Explanation:

Step1: Recall the area formula of a rectangle

The area formula of a rectangle is \(A = l\times w\) (where \(l\) is the length and \(w\) is the width).

Step2: Analyze the effect of increasing length

Assume the width \(w\) remains constant. Let the original length be \(l_1\) and the new length be \(l_2\) with \(l_2>l_1\). The original area \(A_1 = l_1\times w\), and the new area \(A_2=l_2\times w\). Since \(l_2 > l_1\) and \(w>0\), by the property of multiplication of positive numbers (\(A_2 - A_1=(l_2 - l_1)\times w>0\)), the area increases.

Answer:

increase