solving inequalities - The height of a rectangle is less than 10. If the width of the rectangle is increased by 2 and its height is decreased by 1, then its area is increased by 4. What can you say about the width of the original rectangle?

rupa Reddy (last edited 2 years ago) (Teacher, UG1 Grade)

Let the width, height and area of the original rectangle be w, h and A respectively⇒ A = wh

When the width of a rectangle is increased by 2 and its height is decreased by 1, its area is increased by 4

⇒ (w + 2)(h − 1) = A + 4

⇒ wh − w + 2h − 2 = wh + 4⇒ -w + 2h − 2 = 4⇒ w = 2h − 6

But h < 10

Then w < 2 × 10 − 6 ⇒ w < 14

So the width of the original rectangle is less than 14.