Question

Tom decides to sell flowers and vegetables at the market, so he makes two rectangular gardens. The flower garden is 3 meters longer than it's wide. The length of the vegetable garden is 4 meter more than double its width. The combined perimeter of the garden is 126 meters.

Tom decides to fence both gardens to keep out his pigs. The fencing for the flower garden costs $5 per metres. The total fencing costs for the two gardens is $584. Find the dimensions of each gardens.

Answer 1

.....Let x be the width of the flower garden in meters; the length of this garden: (x + 3) meters.

For the vegetable garden, the width is also x meters, and the length: (2x + 4) meters.

The perimeter of the flower garden is given by:

Flower garden perimeter = 2 * 2 * ((x + 3) + x) = 2 * (2x + 3) = 4x + 6 meters

The perimeter of the vegetable garden is given by:

Vegetable garden perimeter = 2 * ((2x + 4) + x) = 2 * (3x + 4) = 6x + 8

the sum of the perimeters of the two gardens is 126 meters

4x+6+6x+8=126

10x+14=126

10x=126-14

x=11.2

we calculate the dimensions of each land:

vegetable garden :

l=x=11.2m

length=2x+4=26.4m

flower garden

l=x= 11.2m

length = x+3= 11.2+3 =14.2m

According to the calculations, the total cost of the fences for the two gardens is $660, not $584. Please check the information provided to make sure everything is correct

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