ASHLEY9801
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∆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 ____.

Respuesta :

jhonyy9
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 
calculista

we know that


1) scale factor is equal to [tex] \frac{1}{10} [/tex]


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=[tex] \frac{1}{10}*40 [/tex]

the longest side of ∆ABC=[tex] 4 [/tex] units


the answer part a) is

the longest side of ∆ABC is [tex] 4 [/tex] units


Part b)

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

so

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


therefore


the answer part b) is

The ratio of the area of ∆ABC to the area of ∆DEF is [tex] \frac{1}{100} [/tex]

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