Question

An architect designs a rectangle 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 dimension of the garden.

Answer 1

width = w
height = h

so w = (2/3) * h

(The perimeter surrounding it)
2w + 2h = 310

2((2/3) * h) + 2h = 310

4h/3 + 2h = 310

10h/3 = 310

10h = 930
h = 93 feet

w = (2/3) * 93

w = 62 feet

Answer 2

The dimension of length is 93 feet and dimension of width is 62 feet.

Explanation:

Consider the provided information.

Let W represents the width of the rectangle flower garden and L represents the length.

It is given that An architect designs a rectangle flower garden such that the width is exactly two thirds of the length.

This can be written as:

W=2/3L

It is given that the length of fence is 310 feet, that means the perimeter of the rectangle is 310.

Perimeter = 2(L+W)

Substitute the respective values in the above formula.

`310 = 2(L+(2)/(3)L)`

`155 = L+(2)/(3)L`

`155 = (3L+2L)/(3)`

`155 = (5L)/(3)`

`465 = 5L`

`L= 93`

Substitute the value of L in W=2/3L.

`W=(2)/(3)* 93`

`W=2* 31`

`W=62`

Hence, the dimension of length is 93 feet and dimension of width is 62 feet.