Question

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 400 feet of antique picket fencing are to be used to enclose the garden, find

the dimensions of the garden.

Answer 1

`10√(6)` feet by
`(20)/(3)√(6)` ft

Explanation:

If the length is
`l`, then the width is
`(2)/(3)l`.

Using the formula for the area of a rectangle,

`l \cdot (2)/(3)l=400 \\ \\ (2)/(3)l^2=400 \\ \\ l^2=600 \\ \\ l=10√(6)[ \\ \\ \implies w=(20)/(3)√(6)`