Question
A triangle two legs are 12 and x then the slant in 13
Answers
GPT-4o mini
To analyze the triangle with legs of lengths 12 and \( x \), and a hypotenuse (slant height) of length 13, we can use the Pythagorean theorem. The theorem states that for a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \):
\[
a^2 + b^2 = c^2
\]
In this case, let's assign:
- \( a = 12 \)
- \( b = x \)
- \( c = 13 \)
Plugging in the values into the Pythagorean theorem gives:
\[
12^2 + x^2 = 13^2
\]
Calculating the squares, we get:
\[
144 + x^2 = 169
\]
Now, we can solve for \( x^2 \) by subtracting 144 from both sides:
\[
x^2 = 169 - 144
\]
\[
x^2 = 25
\]
Next, we take the square root of both sides to find \( x \):
\[
x = 5
\]
So, the length of the other leg \( x \) is 5. Thus, the triangle has legs of lengths 12 and 5, with the hypotenuse measuring 13.
\[
a^2 + b^2 = c^2
\]
In this case, let's assign:
- \( a = 12 \)
- \( b = x \)
- \( c = 13 \)
Plugging in the values into the Pythagorean theorem gives:
\[
12^2 + x^2 = 13^2
\]
Calculating the squares, we get:
\[
144 + x^2 = 169
\]
Now, we can solve for \( x^2 \) by subtracting 144 from both sides:
\[
x^2 = 169 - 144
\]
\[
x^2 = 25
\]
Next, we take the square root of both sides to find \( x \):
\[
x = 5
\]
So, the length of the other leg \( x \) is 5. Thus, the triangle has legs of lengths 12 and 5, with the hypotenuse measuring 13.