Question

The length of a rectangle is 3 less than the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by two. Show your work.

Answer 1

At the beggining, if we called "b" to the length and "h" to the width, then the Area(A) = (h - 3) x (h) = h² - 3h.

In the final situation A = h² - 4

Explanation:

Given A= b x h. At the beggining we have b = h -3 and h. So, A = (h - 3) x h ⇒ A = h² - 3h

In the second situation, b = (h - 3) + 5 and h= h - 2.

Then A= ((h - 3) + 5) x (h - 2) = (h - 3 + 5) x (h - 2) = (h + 2) x (h - 2)

⇒ A= h² - 2h + 2h - 4 ⇒ A= h² - 4.