### Home > CC2MN > Chapter 4 > Lesson 4.4.3 > Problem4-152

4-152.

The perimeter of one shape is $5.5$ times larger than the perimeter of a similar shape.

1. How many times larger are the sides of the large shape than the corresponding sides of the smaller shape?

According to the Math Notes box from Lesson 4.4.2:

The perimeter ratio is $\left(\frac{\text{new perimeter}}{\text{original perimeter}}\right)=\text{scale factor}$.

Find the perimeter of the two example shapes in the Math Notes box and check that the relationship follows this same rule.

2. How many times larger is the area?

According to the Math Notes box from Lesson 4.4.2:

The area ratio is $\left(\frac{\text{new area}}{\text{orginal area}}\right)=\left(\text{scale factor}\right)^2$.

Find the area of the two shapes in the Math Notes box and check that the relationship follows this rule. What did you find?

$30.25$
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