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zysi [14]
4 years ago
12

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.​
Mathematics
1 answer:
allsm [11]4 years ago
8 0

Answer:

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

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