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Pythagorean Triples Practice
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Question
The size of a TV is the diagonal length of the TV. Use a Pythagorean triple to find the length of a 20-inch TV, given that its width is 12 inches.(1 point)
inches
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GPT-4o mini
To find the length of the TV using the Pythagorean theorem, we can represent the situation with a right triangle where:
- The diagonal (the TV size) is 20 inches.
- One leg (width) is 12 inches.
- The other leg (length) is what we need to find.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) is one leg (width = 12 in),
- \(b\) is the other leg (length = unknown),
- \(c\) is the hypotenuse (diagonal = 20 in).
Now, substituting the known values:
\[
12^2 + b^2 = 20^2
\]
Calculating the squares:
\[
144 + b^2 = 400
\]
Now, subtract 144 from both sides to solve for \(b^2\):
\[
b^2 = 400 - 144
\]
\[
b^2 = 256
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{256} = 16
\]
Thus, the length of the TV is **16 inches**.
- The diagonal (the TV size) is 20 inches.
- One leg (width) is 12 inches.
- The other leg (length) is what we need to find.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) is one leg (width = 12 in),
- \(b\) is the other leg (length = unknown),
- \(c\) is the hypotenuse (diagonal = 20 in).
Now, substituting the known values:
\[
12^2 + b^2 = 20^2
\]
Calculating the squares:
\[
144 + b^2 = 400
\]
Now, subtract 144 from both sides to solve for \(b^2\):
\[
b^2 = 400 - 144
\]
\[
b^2 = 256
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{256} = 16
\]
Thus, the length of the TV is **16 inches**.