Question

Length of the sides of a rectangular garden are in the ratio 1:2. Line reconnecting the centre of the adjacent sides of the garden is 20m long. Calculate the perimeter and the area of the garden

Answer 1

Explanation:

Let's assume the length of the shorter side of the rectangular garden is x, then the length of the longer side will be 2x.

The distance between the centres of the adjacent sides of the garden is the hypotenuse of a right-angled triangle whose other two sides are x and 2x/2 = x.

Therefore, by the Pythagorean theorem:

(√(x^2 + x^2))^2 = (20)^2

2x^2 = 400

x^2 = 200

x = √(200) ≈ 14.14

So the length of the shorter side is approximately 14.14 meters, and the length of the longer side is approximately 28.28 meters.

The perimeter of the garden is:

2(shorter side + longer side) = 2(14.14 + 28.28) = 84.84 meters

The area of the garden is:

shorter side × longer side = 14.14 × 28.28 = 400 square meters