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

Blank 1: 4

Blank 2: 1 : 100

Explanation:

I got it right on Edmentum

Hook me up with a 5 star and a Thanks :)

Answer 2

As both triangles are similar, with DEF 10 times the size of ABC based on ratio 1:10. As DEF longest side is 40, ABC longest side will be 1/10 of this value, = 4 (Answer 1)

The ratio of areas of two similar triangles is the square of the ratio of their sides. In this case the ratio of sides between both triangles is 10 / 1 = 10, therefore the ratio of areas is 10² = 100 (answer 2). I.e. Triangle DEF has an area 100x that of ABC.