Unit 6 Pythagorean Theorem Quiz Review

• The sum of the square root of a and b should be equal to the the square of c.

• The sum of the square root of a and b should be equal to the the square root of c.

• The sum of the square of a and b should be equal to the the square root of c.

• The sum of the square of a and the square of b should be equal to the the square of c.

Answer explanation

Eli's formula is incorrect because it states that the sum of the squares of a and b equals the square root of c. The correct relationship is that the sum of the squares of a and b should equal the square of c, as stated in the Pythagorean Theorem.

Cecilia wants to explain the converse of the Pythagorean Theorem using the figure to the right. To do so, what must be true about the figure?

• (area of square a)(area of square b) = area of square c

• area of square a + area of square b = area of square c

• (area of square a)^2 = (area of square b)^2

Answer explanation

The converse of the Pythagorean Theorem states that if the sum of the areas of squares on two sides equals the area of the square on the hypotenuse, then the triangle is a right triangle. Thus, area of square a + area of square b = area of square c is correct.

What is the formula for Pythagorean theorem?

• a²⁺b²=c²

• 2a+2b=2c

• a-b=c

• c-a=c

Answer explanation

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Thus, the correct formula is a² + b² = c².

Tags

CCSS.HSG.SRT.B.4

CCSS.HSG.SRT.C.8

Based on your knowledge of the Pythagorean Theorem, which statement is correct?

• The empty square has a side length of 11 and an area of 121 square units.

• The empty square has a side length of 7 and an area of 49 square units.

• The empty square has a side length of 13 and an area of 169 square units.

• The empty square has a side length of 17 and an area of 289 square units.

Answer explanation

The correct choice is that the empty square has a side length of 13, which gives an area of 13 x 13 = 169 square units. This matches the properties of a square, confirming it as the right answer.

In a right triangle, if one leg measures 5 units and the hypotenuse measures 13 units, what is the length of the other leg?

• 8 units

• 10 units

• 15 units

• 12 units

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where a = 5 and c = 13. We find b² = 13² - 5² = 169 - 25 = 144. Thus, b = √144 = 12. The length of the other leg is 12 units.

The baseball diamond of a little league field measures 60 feet on each side. If the pitcher’s mound is halfway between home plate and second base, how far is the pitcher’s mound from home plate?

• 30.0 ft.

• 42.4 ft.

• 60.0 ft.

• 84.9 ft.

Answer explanation

The distance from home plate to second base is the diagonal of a square with sides of 60 ft. Using the Pythagorean theorem, the distance is 60√2 ft. The pitcher's mound is halfway, so it's 60√2 / 2 = 42.4 ft from home plate.

The size of a TV is measured by the distance diagonally across the screen. What is the height of the TV screen?

• 8 in.

• 122 in.

• 40 in.

• 31.2 in.

Answer explanation

The height of a TV screen can be calculated using the aspect ratio. For a typical 16:9 TV, if the diagonal is 40 in., the height is approximately 31.2 in. Thus, the correct answer is 31.2 in.

Ramesh normally walks 18 yards north on Hampton Drive and 80 yards west on Stillwater Lane. How much shorter would his walk be if he took a shortcut directly to his destination?

• 82 yds.

• 16yds.

• 98 yds.

• 89 yds.

Answer explanation

Ramesh's walk forms a right triangle with legs of 18 yards and 80 yards. The shortcut is the hypotenuse, calculated as √(18² + 80²) = 82 yds. His original walk is 98 yds (18 + 80). The difference is 98 - 82 = 16 yds, so the shortcut is 62 yds shorter.

A ladder is leaning against a wall. The foot of the ladder is 9 feet away from the wall, and the ladder reaches a height of 12 feet on the wall. What is the length of the ladder?

• 18 ft.

• 15 ft.

• 21 ft.

• 10 ft.

Answer explanation

Using the Pythagorean theorem, where the ladder is the hypotenuse: length^2 = height^2 + distance^2. Thus, length^2 = 12^2 + 9^2 = 144 + 81 = 225. Therefore, length = √225 = 15 ft.