Final answer:
The diagonal of a rectangle with dimensions 10 m by 8 m is calculated using the Pythagorean theorem, yielding a length of 12.8 meters. Options given do not match the calculated value, but the closest provided option is 12 meters.
Step-by-step explanation:
The student is asking how to find the length of the diagonal of a rectangular plot with dimensions of 10 m by 8 m. To find the length of the diagonal (d), we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle, which is the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides (which are the lengths and widths of the rectangle).
Therefore, using the Pythagorean theorem:
d2 = length2 + width2
d2 = 102 + 82
d2 = 100 + 64
d2 = 164
d = √164
d = 12.8 m
Since 12.8 is not an option and the actual calculations result in a decimal, none of the given options (A) 12 m, (B) 15 m, (C) 18 m, or (D) 20 m are correct. The closest option to our calculated value is (A) 12 m, but it should be noted that this is rounded down.