Question

1. this rectangle has an area of 18 and a perimeter of 18

if horatio adds a row of 6 tiles on the side of this rectangle what will the new perimeter be?

Explanation:

Step1: Analyze the original rectangle

From the image, the original rectangle has length \(l = 6\) (number of tiles in length) and width \(w=3\) (number of tiles in width). The perimeter formula for a rectangle is \(P = 2(l + w)\). The original perimeter \(P_{original}=18\) (given), and \(2(6 + 3)=18\), which is consistent.

Step2: Determine the new dimensions

When a row of 6 tiles is added on the side (assuming we are changing the width). The new width \(w_{new}=3 + 1=4\) (since each row has 6 tiles, adding 1 row in the width - direction, and length \(l = 6\) remains the same.

Step3: Calculate the new perimeter

Using the perimeter formula \(P=2(l + w)\), substitute \(l = 6\) and \(w_{new}=4\) into the formula. \(P_{new}=2(6 + 4)\)

$$P_{new}=2\times10=20$$

Answer:

\(20\)