Question

this pool is safe to swim in when it contains 9,000 gallons of water.
how long will it take to fill the pool to this level?
problems 4 - 6: an equilateral triangle is a triangle where all three sides have
the same length.

1. complete the table to show the side

lengths and perimeters for several
equilateral triangles.

1. explain why the relationship between

the perimeter and side length for an
equilateral triangle is proportional.

1. what is a constant of proportionality for the relationship?
2. these polygons are scaled copies. determine

the perimeter of the larger polygon. show or
explain your thinking.

Explanation:

Step1: Calculate the perimeter of the smaller polygon

The perimeter of a polygon is the sum of all its side lengths.
For the smaller polygon with side lengths \(7\) cm, \(9\) cm, \(8\) cm, \(11\) cm, and \(6\) cm:

$$P_{small}=7 + 9+8 + 11+6=41$$

Step2: Find the scale factor

The scale factor \(k\) is the ratio of corresponding side lengths. Let's take the top - side lengths: \(k=\frac{13.5}{9}=1.5\)

Step3: Calculate the perimeter of the larger polygon

Since the perimeters of similar polygons are in the same ratio as the scale factor. If \(P_{small}\) is the perimeter of the smaller polygon and \(P_{large}\) is the perimeter of the larger polygon, and \(k\) is the scale factor, then \(P_{large}=k\times P_{small}\)
Substitute \(k = 1.5\) and \(P_{small}=41\)

$$P_{large}=1.5\times41 = 61.5$$

Answer:

The perimeter of the larger polygon is \(61.5\) cm.