Question

1. triangle abc is shown below. its original lengths are multiplied by 150%. what is the new perimeter of abc?

triangle abc with sides ab = 20 cm, bc = 9 cm, ac = 21 cm

Explanation:

Step1: Find original perimeter

First, calculate the original perimeter of triangle \( ABC \) by adding the lengths of its sides. The sides are \( 20 \, \text{cm} \), \( 9 \, \text{cm} \), and \( 21 \, \text{cm} \). So, the original perimeter \( P \) is:
\[
P = 20 + 9 + 21 = 50 \, \text{cm}
\]

Step2: Apply the scale factor

The lengths are multiplied by \( 150\% \), which is equivalent to \( 1.5 \) in decimal form. When the side lengths of a polygon are scaled by a factor \( k \), the perimeter is also scaled by the same factor \( k \). So, the new perimeter \( P' \) is the original perimeter multiplied by \( 1.5 \):
\[
P' = 50 \times 1.5 = 75 \, \text{cm}
\]

Answer:

The new perimeter of \( A'B'C' \) is \( 75 \, \text{cm} \).