Question

A street on a hill slopes upward evenly such that the street rises 1 foot (ft) vertically for every 4 ft traveled horizontally. The bottom of the street is 60 ft lower than the top of the street. How long is the street from the bottom to the top in feet?

A. 15· √(17)
B. 60· √(15)
C. 60· √(17)
D. 240

Answer 1

To determine the length of the street on a hill, the Pythagorean theorem is applied to a right triangle with sides of 60 feet vertical and 240 feet horizontal. The hypotenuse, representing the length of the street, is calculated to be 60 · √(17) feet, which is option C.

Step-by-step explanation:

The question involves solving a problem related to the length of a street on a hill using the concept of right triangles. We know that the street slopes upward, rising 1 foot vertically for every 4 feet traveled horizontally. Because the vertical rise from the bottom to the top of the street is 60 feet, we can determine the length of the street by calculating the hypotenuse of a right-angled triangle where one leg is 60 feet (vertical rise) and the other leg is 240 feet (horizontal distance, calculated as 60 feet × 4).

To find the hypotenuse, we use 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 lengths of the other two sides (a and b). Thus, c = √(a² + b²).

Plugging in the given values, we get:

• a = 60 feet (vertical leg)
• b = 240 feet (horizontal leg)
• c = √(60² + 240²)

Calculating this gives us:

c = √(3600 + 57600) = √61200

c = 60 √(17)

Hence, the length of the street from the bottom to the top is 60 · √(17) feet, which corresponds to option C.