Question

triangle g is a scaled copy of triangle f. what scale factor takes triangle f to triangle g?

Explanation:

Step1: Find the ratio of corresponding sides

We can use the sides of length \(48\) in triangle \(F\) and \(36\) in triangle \(G\). The formula for the scale factor \(k\) is \(k=\frac{\text{length in }G}{\text{length in }F}\).
So, \(k = \frac{36}{48}\)

Step2: Simplify the fraction

Simplify \(\frac{36}{48}\) by dividing both the numerator and the denominator by their greatest - common divisor. The GCD of \(36\) and \(48\) is \(12\).
\(\frac{36\div12}{48\div12}=\frac{3}{4}\)

We can also check with another pair of corresponding sides. For the sides of length \(20\) in triangle \(F\) and \(15\) in triangle \(G\), \(k=\frac{15}{20}\). Simplifying \(\frac{15}{20}\) (GCD of \(15\) and \(20\) is \(5\)), \(\frac{15\div5}{20\div5}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)