A rectangular field measures 350 feet by 400 feet. If you wish to go from one corner to the opposite corner, how much shorter is the trip if you walk along the diagonal rather than the edges?
This is a right angle triangle. Use the Pythagorean Theorem, substituting 350 and 400 for a and b.
a^2 + b^2 = c^2
sqrt(350^2+400^2)=531.5ft
350+400= 750ft
750-531.5= 218.5ft
The trip is 218.5ft shorter if you walk diagonally.
James -- why do you think that Neka couldn't figure this out herself from the information I posted?
To find out how much shorter the trip is if you walk along the diagonal instead of the edges, we need to calculate the lengths of both paths.
The path along the edges forms a rectangle, so we can use the formula for the perimeter of a rectangle to find the length of this path. Perimeter of a rectangle = 2 * (length + width).
In this case, the length is 350 feet and the width is 400 feet, so the perimeter of the rectangle is 2 * (350 + 400) = 2 * 750 = 1500 feet.
The path along the diagonal forms the hypotenuse of a right triangle. We can use the Pythagorean theorem to find the length of this path. The Pythagorean theorem states that in a right 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), expressed as c² = a² + b².
In this case, the two sides of the triangle are the length (350 feet) and the width (400 feet) of the rectangle. So the calculation becomes:
c² = 350² + 400²
c² = 122,500 + 160,000
c² = 282,500
To find c, we take the square root of both sides of the equation:
c = √282,500
c ≈ 531.73 feet (rounded to two decimal places)
Therefore, the path along the diagonal is approximately 531.73 feet long, while the path along the edges is 1500 feet long.
To calculate how much shorter the trip is if you walk along the diagonal instead of the edges, we subtract the length of the diagonal path from the length of the path along the edges:
1500 - 531.73 ≈ 968.27 feet (rounded to two decimal places).
So, the trip is shorter by approximately 968.27 feet if you walk along the diagonal instead of the edges.