What is the Pythagorean Theorem?
Pythagorean Theorem Applications

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•
Mathematics
•
8th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
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: c² = a² + b².
2.
FLASHCARD QUESTION
Front
How do you find the length of a missing side in a right triangle?
Back
To find the length of a missing side in a right triangle, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.
3.
FLASHCARD QUESTION
Front
If one side of a right triangle is 6 cm and the other side is 8 cm, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 cm.
4.
FLASHCARD QUESTION
Front
What is the diagonal length of a square with a side length of 10 units?
Back
The diagonal (d) of a square can be found using the formula: d = s√2, where s is the side length. For a side length of 10 units, d = 10√2 ≈ 14.14 units.
5.
FLASHCARD QUESTION
Front
How do you calculate the area of a square?
Back
The area (A) of a square is calculated by squaring the length of one of its sides: A = s².
6.
FLASHCARD QUESTION
Front
What is the relationship between the sides of a 30-60-90 triangle?
Back
In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the 90° angle.
7.
FLASHCARD QUESTION
Front
If a right triangle has legs of lengths 5 cm and 12 cm, what is the length of the hypotenuse?
Back
Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.
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