Answer:
82.5 cm
Step-by-step explanation:
For similar triangles, ratio of perimeter will equal to ratio of sides.
Here we are given that triangles ABC and DEF are similar.
This implies the corresponding sides are proportional.
By corresponding we mean that the longest sides of ABC with the longest side of DEF.
Hence Longest side of ABC/Longest side of DEF = Ratio of sides
= Ratio of perimeter.
Let the longest side of DEF be x.
i.e. 15/x = 2/11
Cross multiply to get
2x = 165
Divide by 2
x = 82.5 cm.
Hence the longest side of Triangle DEF = 82.5 cm.
Verify: Check proportions of longest sides
= [tex]\frac{15}{82.5} =\frac{2}{11}[/tex] which equals ratio of perimeters.
Thus verified.
