find the dimensions

Question

a vegetable garden with an area of 234 sq. ft. is to be fertilized. If the length of the garden is 1 ft. less than 3 times the width, find the dimensions of the garden.

Answer 1

Let's list what we know:

A_rec = l*w

A = 234

l = 3w - 1

 

Now that we have some values, let's put them into our equation:

234 = (3w - 1)w

234 = 3w² - w

0 = 3w² - w - 234

 

Let's try using the quadratic formula to solve

w = ((-b ± √(b² - 4ac))/2a

w = (-(-1)± √((-1)² - 4 * 3 * -234)/2*3

w = (1 ± √(1 + 2808))/6

w = (1 ± √2809)/6

w = (1 ± 53)/6

We can't have a negative length

w = 54/6

w = 9

 

now that we have w, we can solve for l:

l = 3 * 9 - 1

l = 27 -1

l = 26

 

Now we check our answer:

234 = 26 * 9

234 = 234