∆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 .

The length of the longest side of ∆ABC is 4 units.

The ratio of the area of ∆ABC to the area of ∆DEF is 1 : 100

Step-by-step explanation:

The ratio of the perimeter of ∆ABC to the perimeter of ∆DEF is  1 : 10

As perimeter is one dimensional measurement, that means ∆DEF is scaled from ∆ABC  with a scale factor of 10.

Suppose, the length of longest side of ∆ABC is   unit.

So, the length of longest side of ∆DEF

Given that, the longest side of ∆DEF measures 40 units. So....

So, the length of longest side of ∆ABC is 4 units.

Now, Area is a two dimensional measurement.

So, the ratio of the area of ∆ABC to the area of ∆DEF will be:  

the one on the bottom left

step-by-step explanation:

all of the other ones have a specific pattern

the answer is 489

step-by-step explanation: