Question

also take power-up test 7

1. (19) the perimeter of the square equals the perimeter of the regular pentagon. each side of the pentagon is 16 cm. how long is each side of the square?

diagrams of square and regular pentagon

1. (22) diagram this statement. then answer the questions that follow.

four ninths of the 63 fish in the tank were guppies.
a. how many of the fish were guppies?
b. how many of the fish were not guppies?

Explanation:

Question 5

Step1: Calculate pentagon's perimeter

A regular pentagon has 5 equal sides. Each side is 16 cm, so perimeter \( P_{pentagon} = 5 \times 16 \) cm.
\( 5 \times 16 = 80 \) cm.

Step2: Find square's side length

Let the side of the square be \( s \). The perimeter of a square is \( 4s \). Since \( P_{square} = P_{pentagon} = 80 \) cm, we solve \( 4s = 80 \).
Divide both sides by 4: \( s = \frac{80}{4} = 20 \) cm.

Step1: Understand the fraction

We need to find \( \frac{4}{9} \) of 63 fish. To find a fraction of a number, multiply the number by the fraction: \( 63 \times \frac{4}{9} \).

Step2: Simplify the multiplication

Simplify \( 63 \div 9 = 7 \), then \( 7 \times 4 = 28 \).

Step1: Total fish minus guppies

Total fish = 63, guppies = 28. So non - guppies = \( 63 - 28 \).

Step2: Calculate the subtraction

\( 63 - 28 = 35 \).

Answer:

Each side of the square is 20 cm.

Question 6a