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

Answer:

Step-by-step 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.