Final answer:
To find the perimeter of the right-angled garden, we use the Pythagorean theorem to calculate the hypotenuse and then add the lengths of all three sides. The perimeter is 46.2 units.
Step-by-step explanation:
The question asks us to find the perimeter of a garden in the shape of a right triangle with legs measuring 12 and 15 units. To determine the perimeter, we need to find the length of the hypotenuse using 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) is equal to the sum of the squares of the lengths of the other two sides (the two legs). Here's the calculation:
- Leg A = 12 units
- Leg B = 15 units
- Hypotenuse (C) = √(A² + B²) = √(12² + 15²) = √(144 + 225) = √(369) = 19.2 units (rounded to one decimal)
Now that we have the lengths of all three sides, we can sum them up to find the perimeter:
Perimeter (P) = A + B + C
Perimeter (P) = 12 units + 15 units + 19.2 units
Perimeter (P) = 46.2 units
Note that 46.2 units is not one of the original answer choices given, which suggests there may have been a mistake in the recorded options, or there might be a misunderstanding. However, the calculated perimeter is correct based on the given leg measurements.