Question

1. triangles abc and def are similar. find d.

image of two triangles, triangle abc with sides ab=4 cm, ac=5 cm, bc=6 cm; triangle def with side de=8 cm, side ef=d, and other side e
options: 13, 12, 15, 14

Explanation:

Step1: Identify Corresponding Sides

Triangles \(ABC\) and \(DEF\) are similar. Corresponding sides: \(AB = 4\) cm (in \(ABC\)) corresponds to \(DE = 8\) cm (in \(DEF\)), and \(BC = 6\) cm (in \(ABC\)) corresponds to \(EF = d\) (in \(DEF\)).

Step2: Find the Scale Factor

The scale factor from \(ABC\) to \(DEF\) is \(\frac{DE}{AB}=\frac{8}{4} = 2\).

Step3: Calculate \(d\)

Since corresponding sides of similar triangles are proportional, \(d = BC\times\text{scale factor}=6\times2 = 12\) cm.

Answer:

12