Question

triangles abc and def are similar triangles.
diagram: triangle abc with c to a = 4 m, hypotenuse ab = 5 m; triangle def with f to d = 8 m, e to f = 6 m
use this fact to solve the exercise. round to the nearest tenth.
find the perimeter of triangle abc.
blank m

Explanation:

Step1: Find the scale factor

Since triangles \(ABC\) and \(DEF\) are similar, the ratio of corresponding sides is equal. The side \(AC = 4\) m in \(\triangle ABC\) corresponds to \(FD = 8\) m in \(\triangle DEF\). So the scale factor \(k=\frac{AC}{FD}=\frac{4}{8}=\frac{1}{2}\).

Step2: Find the length of \(BC\)

The side \(EF = 6\) m in \(\triangle DEF\) corresponds to \(BC\) in \(\triangle ABC\). Using the scale factor, \(BC = EF\times k = 6\times\frac{1}{2}=3\) m.

Step3: Calculate the perimeter of \(\triangle ABC\)

The sides of \(\triangle ABC\) are \(AC = 4\) m, \(AB = 5\) m, and \(BC = 3\) m. The perimeter \(P\) of a triangle is the sum of its sides, so \(P=AC + AB+BC=4 + 5+3 = 12\) m.

Answer:

\(12\)