Pythagorean Theorem Word Problems

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•
Mathematics
•
6th - 8th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Pythagorean Theorem?
Back
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). It can be expressed as: a² + b² = c².
2.
FLASHCARD QUESTION
Front
How do you find the length of the diagonal of a square?
Back
To find the length of the diagonal (d) of a square with side length (s), use the formula: d = s√2.
3.
FLASHCARD QUESTION
Front
If a square has an area of 81 square centimeters, what is the length of one side?
Back
The length of one side (s) can be found by taking the square root of the area: s = √81 = 9 cm.
4.
FLASHCARD QUESTION
Front
What is the distance formula derived from the Pythagorean Theorem?
Back
The distance (d) between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).
5.
FLASHCARD QUESTION
Front
How do you determine if a triangle is acute, right, or obtuse using side lengths?
Back
Use the Pythagorean Theorem: If a² + b² = c², the triangle is right; if a² + b² > c², it is acute; if a² + b² < c², it is obtuse.
6.
FLASHCARD QUESTION
Front
What is the height of a right triangle if the base is 8 feet and the hypotenuse is 10 feet?
Back
Using the Pythagorean Theorem: h² + 8² = 10²; h² + 64 = 100; h² = 36; h = 6 feet.
7.
FLASHCARD QUESTION
Front
In a right triangle, if one leg is 6 feet and the other leg is 8 feet, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 feet.
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