Question

1. a triangle is shown below. if the image is dilated by a scale factor of 3.5, then what is the perimeter of the new triangle?

Explanation:

Step1: Calculate the perimeter of the original triangle

The perimeter \(P\) of a triangle is the sum of its side lengths. For the given triangle with side lengths \(3m\), \(4m\), and \(5m\), we have \(P = 3 + 4+5\).

$$P=12m$$

Step2: Use the scale - factor to find the perimeter of the new triangle

When a figure is dilated by a scale factor \(k\), the perimeter of the new figure is \(k\) times the perimeter of the original figure. Here, \(k = 3.5\) and the original perimeter \(P_{original}=12m\). So the perimeter of the new triangle \(P_{new}=k\times P_{original}\)

$$P_{new}=3.5\times12$$

$$P_{new}=42m$$

Answer:

The perimeter of the new triangle is \(42m\)