Question

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.

Answer 1

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

Explanation

Suppose, the length of the rectangular garden is $x$ 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.