Final answer:
The perimeter of the square with an area of 1134m² is calculated by finding the square root of the area to get the side length, then multiplying it by 4. The side length as a radical is simplified to 9√14 m, making the perimeter 36√14 m.
Step-by-step explanation:
The question asks us to find the perimeter of a square with an area of 1134m² without using a calculator. To solve this, first we note that the area (A) of a square is equal to the side length (s) squared, i.e., A = s². Hence, to find the side length of the square, we need to find the square root of the area
Given A = 1134m², let's express the side length as a radical:
s = √1134m².
To simplify the radical, we find the prime factors of 1134 which are 2, 3, 3, and 3 (1134 = 2 × 3² × 3²). The largest perfect square factor within 1134 is 3² × 3² = 9 × 9 = 81. Pulling out the square root of 81, we obtain:
s = √(81 × 14)m²
s = 9√14 m.
The perimeter (P) of a square is four times the side length, therefore:
P = 4s
P = 4 × 9√14 m
P = 36√14 m.
Thus the perimeter of the square is 36√14 meters in simplest radical form.