Question

1. two triangles are similar. triangle abc has a side length of 4 cm and the corresponding side in triangle def is 10 cm.

a) what is the scale factor from triangle abc to triangle def? show your work.
c) if another side of triangle abc is 6 cm, what is the corresponding side in triangle def?

Explanation:

Step1: Define scale factor formula

Scale factor = $\frac{\text{Length of side in DEF}}{\text{Length of side in ABC}}$

Step2: Calculate scale factor (a)

Substitute given values: $\frac{10}{4} = \frac{5}{2}$

Step3: Find corresponding side (c)

Multiply ABC side by scale factor: $6 \times \frac{5}{2}$

Step4: Simplify for final value (c)

$6 \times \frac{5}{2} = 15$

Answer:

a) The scale factor from triangle ABC to triangle DEF is $\frac{5}{2}$
c) The corresponding side in triangle DEF is 15 cm