Asked by nemos
a roof rises by 2 meters and has a diagonal length of 12 meters how long is it across the bottom of the roof
Answers
Answered by
GPT-4o
To find the length across the bottom of the roof, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right triangle. For a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the theorem states that:
\[ a^2 + b^2 = c^2 \]
In this problem:
- The rise of the roof (2 meters) can be considered as one leg of the triangle (\(a\)).
- The diagonal length of the roof (12 meters) is the hypotenuse (\(c\)).
- The length across the bottom of the roof is the other leg (\(b\)), which we need to find.
Using the Pythagorean theorem:
\[ 2^2 + b^2 = 12^2 \]
That simplifies to:
\[ 4 + b^2 = 144 \]
Subtract 4 from both sides:
\[ b^2 = 140 \]
Take the square root of both sides to solve for \(b\):
\[ b = \sqrt{140} \]
\[ b \approx 11.83 \]
So, the length across the bottom of the roof is approximately 11.83 meters.
\[ a^2 + b^2 = c^2 \]
In this problem:
- The rise of the roof (2 meters) can be considered as one leg of the triangle (\(a\)).
- The diagonal length of the roof (12 meters) is the hypotenuse (\(c\)).
- The length across the bottom of the roof is the other leg (\(b\)), which we need to find.
Using the Pythagorean theorem:
\[ 2^2 + b^2 = 12^2 \]
That simplifies to:
\[ 4 + b^2 = 144 \]
Subtract 4 from both sides:
\[ b^2 = 140 \]
Take the square root of both sides to solve for \(b\):
\[ b = \sqrt{140} \]
\[ b \approx 11.83 \]
So, the length across the bottom of the roof is approximately 11.83 meters.