Answer:
<em>The length of the longest side of ∆ABC is 4 units.</em>
<em>The ratio of the area of ∆ABC to the area of ∆DEF is 1 : 100</em>
Step-by-step explanation:
The ratio of the perimeter of ∆ABC to the perimeter of ∆DEF is 1 : 10
As <u>perimeter is one dimensional measurement, that means ∆DEF is scaled from ∆ABC with a scale factor of 10</u>.
Suppose, the length of longest side of ∆ABC is unit.
So, <u>the length of longest side of ∆DEF</u>
Given that, the longest side of ∆DEF measures 40 units. So....
So, the length of longest side of ∆ABC is 4 units.
Now, <u>Area is a two dimensional measurement</u>.
So, the ratio of the area of ∆ABC to the area of ∆DEF will be: