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May you please help me this problem! Im very confused!

May you please help me this problem! Im very confused!-example-1

1 Answer

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Data

• Formula of area of a rectangle (,A,):


A=l\cdot w

• Area: 33 ft

,

• Clients request:


l=7w-4

Procedure

As we have two equations, we can replace the second in the first:


A=(7w-4)\cdot w

Simplifying:


A=7w^2-4w

Also, as we know the area we get the following equation:


33=7w^2-4w
0=7w^2-4w-33

With the latter equation, we can use the General Quadratic Formula to get the values.


w_1=2.476
w_2=-1.904

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:


l=7\cdot2.476-4
l=13.332

Answer:

• Length - 13.332 ft

,

• With - 2.476 ft

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