Question
What is the missing length in the triangle below? (1 point)
65
?
25
65
?
25
Answers
Answered by
GPT-4o mini
To find the missing length in a triangle where the sides are given as 65, ?, and 25, we can assume it is a right triangle and use the Pythagorean theorem, which 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.
Let's consider two scenarios:
1. **Hypotenuse is 65:** In this case, let the missing side be \(x\):
\[
x^2 + 25^2 = 65^2
\]
\[
x^2 + 625 = 4225
\]
\[
x^2 = 4225 - 625
\]
\[
x^2 = 3600
\]
\[
x = \sqrt{3600} = 60
\]
2. **Hypotenuse is 25:** In this case, it is impossible because 65 and x cannot be less than 25.
Thus, the missing length in the triangle is **60** if the hypotenuse is 65.
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse (the longest side) and \(a\) and \(b\) are the lengths of the other two sides.
Let's consider two scenarios:
1. **Hypotenuse is 65:** In this case, let the missing side be \(x\):
\[
x^2 + 25^2 = 65^2
\]
\[
x^2 + 625 = 4225
\]
\[
x^2 = 4225 - 625
\]
\[
x^2 = 3600
\]
\[
x = \sqrt{3600} = 60
\]
2. **Hypotenuse is 25:** In this case, it is impossible because 65 and x cannot be less than 25.
Thus, the missing length in the triangle is **60** if the hypotenuse is 65.