Exploring Pythagorean Theorem

To use the Pythagorean Theorem, the triangle MUST be what kind of triangle?

• obtuse

• scalene

• isosceles

• right

Answer explanation

To use the Pythagorean Theorem, the triangle must be a right triangle. This theorem specifically applies to right triangles, where one angle is exactly 90 degrees, allowing the relationship between the sides to be defined.

Tags

CCSS.8.G.B.8

• largest

• smallest

• middle

• first

Tags

CCSS.8.G.B.8

Given the lengths 3", 4", 5", classify the triangle formed and or state that no triangle CAN be formed.

• No triangle

• Acute triangle

• Right triangle

• Obtuse triangle

Answer explanation

The lengths 3", 4", and 5" satisfy the Pythagorean theorem (3² + 4² = 5²), indicating a right triangle. Therefore, the correct classification is a right triangle.

Tags

CCSS.7.G.A.2

If the legs of a right triangle are 16 and 63, what is the length of the hypotenuse?

• 79

• 2112.5

• 65

• 61

Answer explanation

To find the hypotenuse of a right triangle with legs 16 and 63, use the Pythagorean theorem: c = √(a² + b²). Here, c = √(16² + 63²) = √(256 + 3969) = √4225 = 65. Thus, the hypotenuse is 65.

Tags

CCSS.8.G.B.7

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run? Which equation could be used to solve the problem?

Tags

CCSS.8.G.B.8

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

• 111.8 yards

• 115 yards

• 127.3 yards

• 119 yards

Answer explanation

To find the diagonal distance Patrick walks, use the Pythagorean theorem: d = √(width² + length²) = √(50² + 100²) = √(2500 + 10000) = √12500 ≈ 111.8 yards. Thus, the correct answer is 111.8 yards.

Tags

CCSS.8.G.B.8

Find the missing side.

• 48

• 108

• 83.6

• 72

Tags

CCSS.8.G.B.7

Find the missing side.

• 9

• 41

• 6.4

• 3

Tags

CCSS.8.G.B.7

• true

• false

Answer explanation

The statement is true. In a right triangle, the relationship between the sides is given by the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse. Thus, adding a² and b² and taking the square root gives the correct value for c.

Tags

CCSS.8.G.B.8

A ladder is leaning against a wall, reaching a height of 24 feet. If the base of the ladder is 7 feet away from the wall, how long is the ladder?

• 25 feet

• 26 feet

• 24.5 feet

• 23 feet

Tags

CCSS.8.G.B.8