Question

The length of a rectangular garden is 5 feet less than 4 times its width. Its area is 359 square feet. Find the length and width of the garden. Round answers to the nearest tenth of a foot. Show all work.

Answer 1

Given parameters:

Area of the rectangular garden  = 359ft²

Unknown:

length and width of the garden  = ?

To find the length and breadth of the garden, we need to define and know that the area of a rectangle is.

 Area of a rectangle  = Length x Breadth

From the problem statement;

 Let w = width of the rectangular garden

        L = length of the garden;

 Now,

          length of a rectangular garden is 5 feet less than 4 times its width

           L = 4w - 5

Now let us substitute this into the equation;

       Area  = L x w

    359 = (4w - 5)w

           4w² - 5w - 359

Using:

          w = -b ± √b² -  4ac  /  2a

 where b  = -5 , a  = 4  and c = -359

  w  =   -(-5)  ± √-5² - 4(4)(-359)  /  2(4)

 w = 5 ± √25 + 5744 / 8

 w =  5 ± 75.9 / 8

 w  = $\frac{5 + 75.9}{8} or \frac{5 - 75.9}{8}$

  w  = 10.1ft

 The other solution is not possible it will be a negative value. Width value cannot be negative.

So L = 4w - 5  = 4(10.1) - 5 = 35.5ft

The length and breadth of the rectangular are 35.5ft and 10.1ft respectively.