9. A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. Find the length of fence in meters required to enclose one of these fields?
A.130
B.170
C.180
D.200
E.300
Choice A is wrong.
Pythagorean Theorem:
50^2 + 120^2 = diagonal squared
2500 + 14,400 = d^2
16,900 = d^2
130 = d
Add the three sides together to find the perimeter.
300
Correct.
To solve this problem, we need to find the length of the diagonal line that divides the rectangular field into two fields.
We can use the Pythagorean theorem to find the length of the diagonal. The Pythagorean 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.
In this case, the width of the rectangular field (50 meters) and the length of the rectangular field (120 meters) form the two sides of the right triangle. Let's call the length of the diagonal line "d".
Applying the Pythagorean theorem, we have:
d^2 = (50^2) + (120^2)
Simplifying:
d^2 = 2500 + 14400
d^2 = 16900
To find the value of "d", we take the square root of both sides:
d = sqrt(16900)
d = 130
So, the length of the diagonal line is 130 meters. This length represents the fence required to enclose one of the fields.
The correct answer is A. 130 meters.