Respuesta :
Answer:
width of the garden is 50 ft and the length is 70 ft
Step-by-step explanation:
Solution:-
- We will denote the width and and the length of the rectangular garden as:
Width: x
Length: x + 20
- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.
- Recall that the area ( A ) of a rectangle is the product of length and width as follows:
A = Length * width
A = x*( x + 20 )
3500 = x^2 + 20x
x^2 + 20x - 3500 = 0
- Use the quadratic formula to determine the value of ( x ):
[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]
- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft
