Question
Which set of side lengths form a right triangle?
Responses
10 in., 41 in., 40 in.
10 in., 41 in., 40 in.
15 m, 20 m, 25 m
15 m, 20 m, 25 m
7 cm, 8 cm, 10 cm
7 cm, 8 cm, 10 cm
3 ft, 6 ft, 5 ft
Responses
10 in., 41 in., 40 in.
10 in., 41 in., 40 in.
15 m, 20 m, 25 m
15 m, 20 m, 25 m
7 cm, 8 cm, 10 cm
7 cm, 8 cm, 10 cm
3 ft, 6 ft, 5 ft
Answers
Answered by
GPT-4o mini
To determine which set of side lengths forms a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle with sides \( a \), \( b \), and hypotenuse \( c \), the relationship should be:
\[ a^2 + b^2 = c^2 \]
We will check each set of side lengths:
1. **10 in., 41 in., 40 in.**
\( 10^2 + 40^2 = 100 + 1600 = 1700 \)
\( 41^2 = 1681 \)
This does not satisfy the theorem.
2. **15 m, 20 m, 25 m**
\( 15^2 + 20^2 = 225 + 400 = 625 \)
\( 25^2 = 625 \)
This does satisfy the theorem.
3. **7 cm, 8 cm, 10 cm**
\( 7^2 + 8^2 = 49 + 64 = 113 \)
\( 10^2 = 100 \)
This does not satisfy the theorem.
4. **3 ft, 6 ft, 5 ft**
\( 3^2 + 5^2 = 9 + 25 = 34 \)
\( 6^2 = 36 \)
This does not satisfy the theorem.
The only set of side lengths that forms a right triangle is:
**15 m, 20 m, 25 m**
\[ a^2 + b^2 = c^2 \]
We will check each set of side lengths:
1. **10 in., 41 in., 40 in.**
\( 10^2 + 40^2 = 100 + 1600 = 1700 \)
\( 41^2 = 1681 \)
This does not satisfy the theorem.
2. **15 m, 20 m, 25 m**
\( 15^2 + 20^2 = 225 + 400 = 625 \)
\( 25^2 = 625 \)
This does satisfy the theorem.
3. **7 cm, 8 cm, 10 cm**
\( 7^2 + 8^2 = 49 + 64 = 113 \)
\( 10^2 = 100 \)
This does not satisfy the theorem.
4. **3 ft, 6 ft, 5 ft**
\( 3^2 + 5^2 = 9 + 25 = 34 \)
\( 6^2 = 36 \)
This does not satisfy the theorem.
The only set of side lengths that forms a right triangle is:
**15 m, 20 m, 25 m**
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