Please help me to find area

Question

Given that the length of a rectangle is 4x-4 and the width is 11-x, find the area of the rectangle. What dimensions correspond to the largest area?

Let A(x) be the area function for the rectangle. Expand and simplify your answer.

A(x) =

Answer 1

Hi Humar,

Formula for area of any rectangle is:

A= LW

L=Length

W=Width

Here,

L= 4x -4

W= 11 - x

A(x)= (4x-4)(11-x)

Foil that:

A(x) = 44x - 4x² -44 + 4x

Rearrange in descending order and combine like terms:

A (x)= -4x² + 48x - 44

You can leave like this or factor out a -4--not sure how far your teacher wants you to go on simplification but if you factor out a -4:

A(x) = -4(x² - 12x +11)

Factor the inside:

A(x) = -4(x-11)(x-1)

Again, not sure how far your teacher wants you to simplify, but all are viable expressions for the area, and the last is as simplified as can be. I hope this helps.