Mathematics: An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. if 310 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.

An architect designs a rectangular flower garden

tonio638

12.03.2022

The length and width of the garden are 93 feet and 62 feet respectively.

Explanation

Suppose, the length of the rectangular garden is feet.

As the width is exactly two-thirds of the length, so the width of the garden will be: $\frac{2x}{3}$ feet.

310 feet of antique picket fencing are to be used to enclose the garden. It means, the perimeter of the garden is 310 feet.

Formula for perimeter of rectangle = 2(length+width)

So, the equation will be....

$2(x+\frac{2x}{3})= 310\\ \\ x+\frac{2x}{3}= \frac{310}{2}\\ \\ \frac{5x}{3}=155\\ \\ 5x= 465\\ \\ x= \frac{465}{5}=93$

So, the length of the garden is 93 feet and the width is $(\frac{2*93}{3})=62$ feet.

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