Certainly! Let's solve each of these questions step by step.
(i) Find the length of the garden:
Since the garden is square, its area is the square of one of its sides. To find the length of one of the sides, we need to take the square root of the area.
Area of the garden = 1764 square meters
Length of the garden = square root of the area
= sqrt(1764)
= 42 meters
So the length of each side of the square garden is 42 meters.
(ii) Find the length of the diagonal of the garden:
To find the diagonal of the garden, we use the Pythagorean Theorem. In a square the sides are all equal length and the diagonal forms a right-angled triangle with two sides. Hence the diagonal can be computed as:
Diagonal length = sqrt(side^2 + side^2)
= sqrt(42^2 + 42^2)
= sqrt(2 * 42^2)
= sqrt(2 * 1764)
= sqrt(3528)
= 42 * sqrt(2)
≈ 42 * 1.414
≈ 59.4 meters
(iii) Find the ratio between the diagonal and the length of the garden:
Now that we have the lengths of both the diagonal and one side, we can find the ratio by dividing the length of the diagonal by the length of the side.
Ratio = Diagonal length / Side length
= (42 * sqrt(2)) / 42
= sqrt(2) / 1
≈ 1.414 / 1
= 1.414
So, the ratio between the diagonal and the length of the garden is approximately 1.414.
(iv) Find the perimeter of the garden:
The perimeter of a square is the sum of all its sides.
Perimeter = side length * 4
= 42 meters * 4
= 168 meters
Therefore, the perimeter of the garden is 168 meters.
