Question

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?a. 12 in²

b. 48 in²
c. 96 in²

Answer 1

`thank \: you`

Answer 2

Explanation:

The width is shorter than the length. If they are both even integers and they are consecutive as well, then if the width is x, the length is x + 2. That means that if x is any even integer, say 4, adding 2 to it gives you the next even integer which is 4 + 2 = 6. Apply that pattern to any even (or odd!) numbers and you will find that it is the general rule. So we have:

w: x

l: x + 2

It says that "if the width is decreased by 3" then the area is 24. If the width is x, then decreasing that by 3 is x - 3. The area formula for a rectangle is length times width, so we have:

`(x+2)(x-3)=24`

FOIL that out to get

`x^2-x-6=24`

Subtract the 24 from both sides and then factor:

`x^2-x-30=0` so

x = -5, 6

Since length (and time!) are the only 2 things in math that will NEVER EVER BE NEGATIVE we can disregard the -5. That means that the width is 6 inches. Plugging that back into the original rectangle, we get that the width is 6 and the length is 6 + 2 or 8. 6 times 8 = 48. That's the area of the original rectangle.