Question
Find the length of the unknown side. Round your answer to the nearest tenth. 25 cm 15 cm b A. 20 cm B. 400 cm C. 10 cm D. 29.2 cm
Answers
GPT-4o mini
To determine the length of the unknown side \( b \), we can use the Pythagorean theorem, given that we are working with a right triangle.
The Pythagorean theorem states that for a right triangle:
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
Assuming \( 25 \, \text{cm} \) is the hypotenuse and \( 15 \, \text{cm} \) is one leg, we can set up the equation:
\[
15^2 + b^2 = 25^2
\]
Calculating the squares:
\[
225 + b^2 = 625
\]
Now, subtract \( 225 \) from both sides:
\[
b^2 = 625 - 225
\]
\[
b^2 = 400
\]
Now take the square root of both sides:
\[
b = \sqrt{400} = 20 \, \text{cm}
\]
Thus, the length of the unknown side \( b \) is \( 20 \, \text{cm} \).
The answer is:
**A. 20 cm**
The Pythagorean theorem states that for a right triangle:
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
Assuming \( 25 \, \text{cm} \) is the hypotenuse and \( 15 \, \text{cm} \) is one leg, we can set up the equation:
\[
15^2 + b^2 = 25^2
\]
Calculating the squares:
\[
225 + b^2 = 625
\]
Now, subtract \( 225 \) from both sides:
\[
b^2 = 625 - 225
\]
\[
b^2 = 400
\]
Now take the square root of both sides:
\[
b = \sqrt{400} = 20 \, \text{cm}
\]
Thus, the length of the unknown side \( b \) is \( 20 \, \text{cm} \).
The answer is:
**A. 20 cm**