Question

an architect designs a rectangular flower garden such that the width is exactly two - thirds of the length. if 350 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. what is the length of the garden? the length of the garden is

Explanation:

Step1: Define variables

Let the length of the garden be $l$ feet and the width be $w$ feet. Given $w=\frac{2}{3}l$.

Step2: Set up perimeter equation

The perimeter of a rectangle is $P = 2(l + w)$. We know that $P=350$ feet. Substitute $w=\frac{2}{3}l$ into the perimeter - formula: $350 = 2(l+\frac{2}{3}l)$.

Step3: Simplify the equation

First, simplify the right - hand side: $l+\frac{2}{3}l=\frac{3l + 2l}{3}=\frac{5l}{3}$. So the equation becomes $350 = 2\times\frac{5l}{3}=\frac{10l}{3}$.

Step4: Solve for $l$

Multiply both sides of the equation $\frac{10l}{3}=350$ by $\frac{3}{10}$: $l = 350\times\frac{3}{10}=105$ feet.

Step5: Solve for $w$

Since $w=\frac{2}{3}l$, substitute $l = 105$ into the equation: $w=\frac{2}{3}\times105 = 70$ feet.

Answer:

The length of the garden is 105 feet and the width is 70 feet.