Pythagorean Applications Quiz

Charlotte and Harper are building a treehouse. They need to determine which of the following triangles is a right-angled triangle to ensure the stability of the structure. Which one should they choose?

• A) A triangle with sides 3 cm, 4 cm, and 5 cm

• B) A triangle with sides 5 cm, 5 cm, and 5 cm

• C) A triangle with sides 6 cm, 8 cm, and 9 cm

• D) A triangle with sides 7 cm, 24 cm, and 26 cm

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DOK Level 1: Recall

Kiara and Neha are building a ramp for their school project. If the ramp forms a right-angled triangle with legs of lengths 6 cm and 8 cm, what is the length of the hypotenuse?

• A) 10 cm

• B) 12 cm

• C) 14 cm

• D) 15 cm

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DOK Level 1: Recall

Aarav is using a ladder to paint a wall. The ladder is leaning against the wall, forming a right-angled triangle with the ground. If the ladder is 5 metres long and the base of the ladder is 3 metres from the wall, how high up the wall does the ladder reach?

• A) 2 metres

• B) 3 metres

• C) 4 metres

• D) 5 metres

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DOK Level 1: Recall

Anaya and Sophia are building a ramp for their school project. Which of the following sets of side lengths can form a right-angled triangle?

• A) 7 cm, 24 cm, 25 cm

• B) 8 cm, 15 cm, 17 cm

• C) 9 cm, 12 cm, 15 cm

• D) All of the above

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DOK Level 1: Recall

Priya and James are planning to walk across a rectangular park that is 50 metres long and 30 metres wide. What is the length of the diagonal path that cuts across the park?

• A) 40 metres

• B) 50 metres

• C) 58 metres

• D) 60 metres

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DOK Level 1: Recall

Liam is building a ramp for his skateboard. He uses three pieces of wood with lengths 9 cm, 12 cm, and 15 cm. Is the ramp a right-angled triangle?

• A) Yes

• B) No

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DOK Level 1: Recall

Rohan is building a ramp for his skateboard. The ramp forms a right-angled triangle with a hypotenuse of 13 cm and one leg of 5 cm. What is the length of the other leg?

• A) 10 cm

• B) 12 cm

• C) 14 cm

• D) 15 cm

Answer explanation

In a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the length of the other leg is sqrt(13^2 - 5^2) = 12 cm (Option B).

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DOK Level 1: Recall

Zoey is designing a square garden with a side length of 8 metres. What is the length of the diagonal of the garden?

• A) 8 metres

• C) 16 metres

Answer explanation

The length of the diagonal of a square can be found using the Pythagorean theorem. Diagonal = side length * sqrt(2). Therefore, the diagonal of the square with a side length of 8 metres is 8√2 metres.

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DOK Level 1: Recall

Aarav is building a triangular garden with sides of lengths 10 cm, 24 cm, and 26 cm. Is this triangle a right-angled triangle?

• A) Yes

• B) No

Answer explanation

The triangle with sides of lengths 10 cm, 24 cm, and 26 cm is a right-angled triangle because it follows the Pythagorean theorem (10^2 + 24^2 = 26^2).

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DOK Level 1: Recall

Rohan and Olivia are measuring a right-angled triangle in their school project. The legs of the triangle are 7 cm and 24 cm. What is the length of the hypotenuse?

• A) 25 cm

• B) 26 cm

• C) 27 cm

• D) 28 cm

Answer explanation

The length of the hypotenuse can be calculated using the Pythagorean theorem: c = √(a^2 + b^2) = √(7^2 + 24^2) = √(49 + 576) = √625 = 25 cm. Therefore, the correct answer is A) 25 cm.

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DOK Level 1: Recall