Asked by p
Use the Pythagorean Theorem to find the missing side of the right triangle. (1 point) Responses 169 cm 169 cm 25 cm 25 cm 144 cm 144 cm 13 cm
Answers
Answered by
GPT-4o mini
To use the Pythagorean Theorem, we recall that it states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side) and \( a \) and \( b \) are the lengths of the other two sides of the right triangle.
From the options provided, we can consider two cases.
1. **If we are looking for the hypotenuse \( c \)**:
Given two sides (let's say \( a = 12 \) cm and \( b = 5 \) cm for instance):
\[ a^2 + b^2 = c^2 \]
If \( 12 \) and \( 5 \) are example values, that would give:
\[ 12^2 + 5^2 = c^2 \]
\[ 144 + 25 = c^2 \]
\[ 169 = c^2 \]
\[ c = \sqrt{169} = 13 \, \text{cm} \]
2. **If we are looking for one of the shorter sides \( a \) or \( b \)**:
If the hypotenuse is \( 25 \) cm and one side \( b = 24 \) cm:
\[ a^2 + 24^2 = 25^2 \]
\[ a^2 + 576 = 625 \]
\[ a^2 = 625 - 576 \]
\[ a^2 = 49 \]
\[ a = \sqrt{49} = 7 \, \text{cm} \]
Given that your response options are \( 169 \, \text{cm} \), \( 25 \, \text{cm} \), \( 144 \, \text{cm} \), and \( 13 \, \text{cm} \), we can conclude that the triangle's dimensions we are working with lead us to \( 13 \, \text{cm} \) being a valid length when finding a side.
Please provide more context if you want specific sides or checks against particular lengths!
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side) and \( a \) and \( b \) are the lengths of the other two sides of the right triangle.
From the options provided, we can consider two cases.
1. **If we are looking for the hypotenuse \( c \)**:
Given two sides (let's say \( a = 12 \) cm and \( b = 5 \) cm for instance):
\[ a^2 + b^2 = c^2 \]
If \( 12 \) and \( 5 \) are example values, that would give:
\[ 12^2 + 5^2 = c^2 \]
\[ 144 + 25 = c^2 \]
\[ 169 = c^2 \]
\[ c = \sqrt{169} = 13 \, \text{cm} \]
2. **If we are looking for one of the shorter sides \( a \) or \( b \)**:
If the hypotenuse is \( 25 \) cm and one side \( b = 24 \) cm:
\[ a^2 + 24^2 = 25^2 \]
\[ a^2 + 576 = 625 \]
\[ a^2 = 625 - 576 \]
\[ a^2 = 49 \]
\[ a = \sqrt{49} = 7 \, \text{cm} \]
Given that your response options are \( 169 \, \text{cm} \), \( 25 \, \text{cm} \), \( 144 \, \text{cm} \), and \( 13 \, \text{cm} \), we can conclude that the triangle's dimensions we are working with lead us to \( 13 \, \text{cm} \) being a valid length when finding a side.
Please provide more context if you want specific sides or checks against particular lengths!