\(\triangle ABC\sim\triangle DEF\). The perimeters of \(\triangle ABC\) and \(\triangle DEF\) are 54 cm and 36 cm respectively. If DE \(=10\) cm, what is the length of AB?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 cm
In similar triangles all corresponding sides are in the same ratio, so the ratio of the perimeters equals the ratio of corresponding sides. AB corresponds to DE.
\(\displaystyle\frac{AB}{DE}=\frac{54}{36}=\frac{3}{2}\)
\(\displaystyle AB=\frac{3}{2}\times10=15\) cm
