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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 ____.

Verified Answer :

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 \(\frac{1}{10}\)


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 \(\frac{1}{100}\)

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