Question

1. two similar triangles have perimeters of 45 cm and 75 cm respectively. what scale factor would relate these two triangles?

Explanation:

Step1: Recall scale - factor formula

For similar figures, the scale factor is the ratio of the corresponding linear measurements. Since perimeter is a linear measurement, the scale factor $k$ between two similar triangles is given by the ratio of their perimeters. Let the perimeters be $P_1 = 45$ cm and $P_2=75$ cm. The scale factor $k=\frac{P_1}{P_2}$ (assuming we are going from the smaller - perimeter triangle to the larger - perimeter triangle).
$k=\frac{45}{75}$

Step2: Simplify the ratio

We simplify the fraction $\frac{45}{75}$ by finding the greatest common divisor (GCD) of 45 and 75. The GCD of 45 and 75 is 15. Divide both the numerator and the denominator by 15.
$\frac{45\div15}{75\div15}=\frac{3}{5}$

Answer:

$\frac{3}{5}$