Question

∆ABC is similar to ∆DEF. The ratio of the perimeter of ∆ABC to the perimeter of ∆DEF is 1 : 10. The longest side of ∆DEF measures 40 units. The length of the longest side of ∆ABC is ____units. The ratio of the area of ∆ABC to the area of ∆DEF is ____.

Answer 1

we know that

1) scale factor is equal to $\frac{1}{10}$

2) The ratio of the perimeters of the triangles is equal to the ratio of the measures of the sides

3) the longest side of ∆ABC=[scale factor]*the longest side of ∆DEF

the longest side of ∆ABC=$\frac{1}{10}*40$

the longest side of ∆ABC=$4$ units

the answer part a) is

the longest side of ∆ABC is $4$ units

Part b)

The ratio of the area of ∆ABC to the area of ∆DEF is equal to the scale factor squared

so

$[scale factor]^{2} =(\frac{1}{10})^{2} \\ \\ =\frac{1}{100} \\ \\ =0.01$

therefore

the answer part b) is

The ratio of the area of ∆ABC to the area of ∆DEF is $\frac{1}{100}$

Answer 2

Bc. the ratio of the perimeters is 1:4 so this will be ratio of sides too so than the longest side of triangle DEF measures 40 units so the length of longest side of triangle ABC will measure 40/10 = 4 units 

hope this will help you