lenghts of the sides of a rectangular garden are in a ratio 1:2. Line connecting the centers of the adjacent sides of the garden is 20 m long. Calculate the perimeter and the area of the garden.

perimeter = 107.4 m

area = 640.82 m²

Step-by-step explanation:

The line connecting the the centers of the adjacent sides of the garden is 20 m long. The line is a diagonal that forms an hypotenuse sides of a triangle.

The length of side of the rectangle has a ratio of 1 : 2. This means one side has a length a meters and the other 2a meters.

Pythagoras theorem can be use to get a since a right angle is formed due to the diagonal.

(a/2) ² + (2a/2) ² = 20²

(a/2) ² + (a) ² = 20²

a²/4 + a² = 400

(a² + 4a²) / 4 = 400

5a²/4 = 400

cross multiply

5a² = 1600

a² = 1600/5

a² = 320

square root both sides

a = √320

a = 17.88854382

a ≈ 17.90

The required length is a = 17.90 m and the other side will be 17.90 * 2 = 35.80 m.

Area = length * breadth

area = 17.90 * 35.80 = 640.82 m²

perimeter = 2 (l + b)

perimeter = 2 (35.80 + 17.90)

perimeter = 2 (53.7)

perimeter = 107.4 m