Springdale Street and Oakdale Avenue intersect. If Springdale Street is 6 meters wide and Oakdale Avenue is 6 meters wide, what is the distance between two opposite corners of the intersection? If necessary, round to the nearest tenth.
Question
Springdale Street and Oakdale Avenue intersect. If Springdale Street is 6 meters wide and Oakdale Avenue is 6 meters wide, what is the distance between two opposite corners of the intersection? If necessary, round to the nearest tenth.
Solution
To find the distance between two opposite corners of the intersection, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, the width of Springdale Street and Oakdale Avenue form the two sides of a right triangle, and the distance between two opposite corners of the intersection is the hypotenuse.
Given that both Springdale Street and Oakdale Avenue are 6 meters wide, we can substitute these values into the Pythagorean theorem:
(6m)^2 + (6m)^2 = c^2
36m^2 + 36m^2 = c^2
72m^2 = c^2
Taking the square root of both sides to solve for c (the hypotenuse), we get:
c = sqrt(72m^2)
c = 8.49 meters
So, the distance between two opposite corners of the intersection is approximately 8.5 meters, rounded to the nearest tenth.
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