Question

emily is comparing two similar triangles. triangle rst has sides 5 c and 13 cm. triangle xyz has sides 10 cm, y cm, and 26 cm. question 4 what is the scale factor from triangle rst to triangle xyz? 1.5 2 3 1

Explanation:

Step1: Recall the scale - factor formula

The scale factor \(k\) from triangle \(RST\) to triangle \(XYZ\) is given by \(k=\frac{\text{side of }XYZ}{\text{side of }RST}\) for corresponding sides.

Step2: Identify corresponding sides

Assume the sides \(5\) cm (of \(RST\)) and \(10\) cm (of \(XYZ\)) are corresponding, and \(13\) cm (of \(RST\)) and \(26\) cm (of \(XYZ\)) are corresponding.
For the pair of sides \(a = 5\) (from \(RST\)) and \(A=10\) (from \(XYZ\)), the scale factor \(k=\frac{A}{a}\).
Substitute \(a = 5\) and \(A = 10\) into the formula: \(k=\frac{10}{5}\).
For the pair of sides \(b = 13\) (from \(RST\)) and \(B = 26\) (from \(XYZ\)), the scale factor \(k=\frac{B}{b}\). Substitute \(b=13\) and \(B = 26\) into the formula: \(k=\frac{26}{13}\).

Answer:

\(2\)