Answer:
Distance between opposite corners = 95 meters
Explanation:
Because this is a rectangle, the distance between opposite corners of the field is essentially the length of the diagonal.
The diagonals of rectangles are congruent, so we only have to find the length of one diagonal.
Remember that rectangles have four right angles in their corners
The diagonal, the length, and width of a rectangle make a right triangle, where the diagonal is the hypotenuse (i.e., side opposite the right angle).
Thus, we can find the length of the diagonal using the Pythagorean theorem, which is given by:
a^2 + b^2 = c^2, where
- a and b are the shorter sides of the triangle called legs (in this case, the legs are the length and width of the rectangle),
- and c is the hypotenuse (in this case, the hypotenuse is the diagonal of the rectangle).
Step 1: Plug in 57 and 76 for a and b in the Pythagorean theorem and simplify on the left-hand side of the equation:
57^2 + 76^2 = c^2
3249 + 5776 = c^2
9025 = c^2
Step 2: Take the square root of both sides to find c, the length of the hypotenuse (aka the distance between opposite corners of the farmer's field):
√(9025) = √(c^2)
95 = c
Thus, the distance between opposite corners of the farmer's field is 95 meters.