SOLUTION: ∆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.
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Question 1036212: ∆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 2 4 16 30 units. The ratio of the area of ∆ABC to the area of ∆DEF is 1 : 1 1 : 2 1 : 10 1 : 100 .
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the ratio of the perimeter is equal to 1/10, therefore the ratio of each of the corresponding sides is 1/10.
if the longest side in triangle DEF is 40, then the longest side in triangle ABC is 4, because 40 is 10 * 4.
the ratio of the area of the similar triangles is equal to the ratio of each of the corresponding sides squared.
(1/10)^2 = 1/100.
the ratio of the area of these 2 similar triangles is 1/100.
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