Data
• Formula of area of a rectangle (,A,):
[tex]A=l\cdot w[/tex]
• Area: 33 ft
,
• Clients request:
[tex]l=7w-4[/tex]
Procedure
As we have two equations, we can replace the second in the first:
[tex]A=(7w-4)\cdot w[/tex]
Simplifying:
[tex]A=7w^2-4w[/tex]
Also, as we know the area we get the following equation:
[tex]33=7w^2-4w[/tex][tex]0=7w^2-4w-33[/tex]
With the latter equation, we can use the General Quadratic Formula to get the values.
[tex]w_1=2.476[/tex][tex]w_2=-1.904[/tex]
We have to take the positive value as the with cannot be negative.
Finally, replacing this value in the second equation we get the length:
[tex]l=7\cdot2.476-4[/tex][tex]l=13.332[/tex]
Answer:
• Length - 13.332 ft
,
• With - 2.476 ft
