Question

chapter 3: pythagorean relationship practice test
phase 1: easy levels (questions 1-6)
focus: squares, square roots, estimating, and basic right triangle vocabulary.

1. a square floor tile has a side length of \\(9\text{ cm}\\). what is the area of the surface of this tile?

1. a square-shaped garden plot has a total surface area of \\(64\text{ m}^2\\). what is the perimeter of this garden?

1. the number \\(45\\) is not a perfect square. between which two consecutive whole numbers does the value of \\(\sqrt{45}\\) lie?

1. in a right-angled triangle, the two shorter sides that meet at a \\(90^\circ\\) angle are called the legs. what is the special mathematical name given to the longest side opposite the right angle?

1. a right triangle has legs with lengths of \\(3\text{ cm}\\) and \\(4\text{ cm}\\). write out the equation of the pythagorean theorem (\\(a^2 + b^2 = c^2\\)) substituting these numbers into the correct positions.

1. determine the exact value of \\(\sqrt{121}\\).

Explanation:

Calculate the area of the square tile

$$ \text{Area} = s^2 = 9^2 = 81\text{ cm}^2 $$

Calculate the perimeter of the square garden

$$
LATEXBLOCK0
$$

Estimate the value of \(\sqrt{45}\)

$$
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$$

Identify the right triangle vocabulary and substitute values into the Pythagorean theorem

$$
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$$

Determine the exact value of \(\sqrt{121}\)

$$ \sqrt{121} = 11 $$

Answer:

No.	Answer
2	\(32\text{ m}\)
3	6 and 7
4	Hypotenuse
5	\(3^2 + 4^2 = c^2\)
6	11