Final answer:
The perimeter of the rectangular terrain with a diagonal of 37 meters and a height of 12 meters is calculated using the Pythagorean theorem to first find the length. The length is found to be 35 meters, and the perimeter, using the formula P = 2l + 2w, is found to be 94 meters.
Step-by-step explanation:
The student has given the length of the diagonal of a rectangular terrain, which is 37 meters, and the height (width), which is 12 meters. To find the perimeter, we first need to calculate the length of the rectangle. We can use the Pythagorean theorem, since the diagonal and the sides of the rectangle form a right-angled triangle:
- Pythagorean theorem: a² + b² = c², where c is the diagonal (37 meters), a is the height (12 meters), and b is the length we need to find.
- Solve for b: b² = c² - a² = 37² - 12² = 1369 - 144 = 1225.
- Calculate b: b = √1225 = 35 meters.
Now that we have the length (35 meters) and the height (12 meters), we can calculate the perimeter (P) of the rectangle using the formula:
P = 2l + 2w, where l is the length and w is the width (height).
Perimeter: P = 2(35) + 2(12) = 70 + 24 = 94 meters.
The correct answer for the perimeter of the land is 94 meters, which corresponds to option d).