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?

12 square inches
48 square inches
96 square inches

Answer 1

Greetings!

To solve this problem, we will have to create a linear system:

Let Statements:
Let x represent the width of the first rectangle
Let y represent the length of the first rectangle

Linear System:
We can create the two equations (a system) using the information from the problem:
$\left \{ {{x+2=y} \atop {(x-3)(y)=24}} \right.$

Solve the system using Elimination or Substitution.

Isolate for x, in Equation #1:
$x+2=y$

$x=y-2$

Substitute this value into Equation #2:
$(x-3)(y)=24$

$((y-2)-3)(y)=24$

Simplify the Equation:
$(y-2-3)(y)=24$

$(y-5)(y)=24$

Distribute the Parenthesis:
$(((y)(y))-(5)(y))=24$

$y^2-5y=24$

Add -24 to both sides:
$(y^2-5y)+(-24)=(24)+(-24)$

$y^2-5y-24=0$

Factor the Simple Trinomial:
$y^2-8y+3y-24=0$

$y(y-8)+3(y-8)=0$

$(y-8)(y+3)=0$

Set Factors to equal 0:

First Factor:
$y-8=0$

$y=8$

Second Factor:
$y+3=0$

$y=-3$

Since it is impossible to have a "negative length" the only possible answer would be:
$\boxed{y=8}$

Using this value, find the value of x:
$x+2=y$

$x+2=(8)$

Add -2 to both sides:
$(x+2)+(-2)=(8)+(-2)$

$\boxed{x=6}$

To find the area of the first rectangle, we can use a formula:
$A_{Rectangle}=(l)(w)$

Input the values:
$A_{Rectangle}=(8)(6)$

Simplify:
$A_{Rectangle}=48$

The Area of the First Rectangle is:
$\boxed{=48in^2}$

I hope this helped!
-Benjamin

Answer 2

Answer:

Credit from the first person. The Answer is 48^2 inches

Step-by-step explanation: