Final answer:
Using the Pythagorean theorem, the length of the ramp's wooden surface, which is the hypotenuse of the right triangle made by the rise and horizontal distance, is approximately 6.18 meters. The closest given option is 6.08 meters, which may indicate a typo in the provided options.
Step-by-step explanation:
To find the length of the wooden surface of the ramp that Leila is building for her grandma's house, we need to understand that we're dealing with a right triangle. The rise of the ramp forms one leg of the triangle (the vertical leg), the horizontal distance forms the other leg (the horizontal leg), and the wooden surface of the ramp is the hypotenuse.
The vertical rise is 1.5 meters and the horizontal distance is 6 meters. Applying the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), we get:
c² = a² + b²
c² = 1.5² + 6²
c² = 2.25 + 36
c² = 38.25
By taking the square root of both sides to solve for c, we find that:
c = √38.25
Therefore, the length of the ramp's wooden surface is:
c ≈ 6.18 meters
So, the closest option to the exact answer is OPTION 1: 6.08 meters, although the actual length calculated is 6.18 meters, not an option provided, indicating there might be a typo or mistake in the question or options provided.