north avenue is 36ft wide when it ends at main st. a 45 foot long diagonal crosswal allows pedestrians to cross main st to or from either corner of north ave. determine the width of main st.
Pythagorean Theorem:
a^2 + b^2 = c^2
36^2 + b^2 = 45^2
1296 + b^2 = 2025
b^2 = 729
b = 27 feet
To determine the width of Main St., we can use the Pythagorean Theorem to find the length of the segment of North Ave. that intersects with Main St.
Let's represent the width of Main St. as 'x'.
According to the given information:
- North Ave. is 36 feet wide.
- There is a diagonal crosswalk that connects two corners of North Ave. and spans 45 feet crossing Main St.
Using the Pythagorean Theorem, we have:
(Width of North Ave.)^2 + (Width of Main St.)^2 = (Diagonal of the Crosswalk)^2
Plugging in the given measurements:
36^2 + x^2 = 45^2
Simplifying the equation:
1296 + x^2 = 2025
Subtracting 1296 from both sides:
x^2 = 2025 - 1296
x^2 = 729
To solve for 'x', we take the square root of both sides:
x = √729
x = 27 feet
Therefore, the width of Main St. is 27 feet.