### Home > MC2 > Chapter 9 > Lesson 9.3.3 > Problem9-107

9-107.

A triangle is enlarged by a scale factor of $\frac { 10 } { 3 }$.

1. If the perimeter of the enlargement is $36$ m, find the perimeter of the original triangle.

According to the Math Notes box from Lesson 9.2.2:
The perimeter ratio is $(\frac{\text{ new perimeter }}{\text{ original perimeter}})=$ scale factor.

$\text{What original perimeter times the scale factor }\frac{10}{3} \text{ equals the enlarged perimeter of 36 m?}$

This can be represented by the following equation with the original perimeter defined as $x$.
$\frac{10}{3} x = 36$

2. If the area of the enlarged triangle is $25$ square meters, what is the area of the original triangle?

According to the Math Notes box from Lesson 9.2.2:
The area ratio is $(\frac{\text{ new perimeter }}{\text{ original perimeter}})=(\text{scale factor})^2$$\text{What would the area be if the scale factor is } \frac{10}{3} ?$.

$\text{If the area ratio is } \frac{100}{9} \text{, create an expression like the one given above to solve for the original area.}$

$2.25$ square meters