Question

1. jayce is considering the rectangle shown.

the length of each side is increased by 2 units. jayce says that would double the perimeter of the rectangle. is he correct?
options:
yes, jayce is correct. in order each side length has to be inc
yes, jayce is correct. in order each side length has to be dou
no, jayce is incorrect. in order each side length has to be doubl

Explanation:

Step1: Calculate original perimeter

The formula for the perimeter of a rectangle is \( P = 2\times (l + w) \), where \( l \) is the length and \( w \) is the width. For the original rectangle, \( l = 12 \) and \( w = 8 \). So, \( P_{original}=2\times(12 + 8)=2\times20 = 40 \).

Step2: Calculate new side lengths

Each side is increased by 2 units. So the new length \( l_{new}=12 + 2 = 14 \) and the new width \( w_{new}=8 + 2 = 10 \).

Step3: Calculate new perimeter

Using the perimeter formula for the new rectangle, \( P_{new}=2\times(14 + 10)=2\times24 = 48 \).

Step4: Compare perimeters

Doubling the original perimeter would be \( 2\times40 = 80 \). But the new perimeter is 48, which is not equal to 80. So Jayce is incorrect. To double the perimeter, each side length has to be doubled (since perimeter is linear in side lengths, doubling each side would double the perimeter: new \( l = 24 \), new \( w = 16 \), \( P_{new}=2\times(24 + 16)=80 \), which is double of 40).

Answer:

No, Jayce is incorrect. In order to double the perimeter, each side length has to be doubled.