Question

The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x2 + 7x + 12.
Factor the trinomial to find the length and width of the rectangle.
l = x + 6; w = x + 2
l = x + 5; w = x + 7
l = x + 4; w = x + 3

Answer 1

Answer:

Option C is correct

$l = x+4$ unit and $w = x+3$ unit

Step-by-step explanation:

Area of a rectangle is given by:

$A =lw$           ....[1]

where

A is the area of rectangle

l is the length of a rectangle

w is the width of a rectangle.

As per the statement:

A certain rectangle has an area of $x^2 + 7x + 12$

⇒$A = x^2+7x+12$

Now factor this trinomial :

$A = x^2+4x+3x+12$

⇒$A = x(x+4)+3(x+4)$

⇒$A=(x+4)(x+3)$ unit square

On comparing with [1] we have;

$l = x+4$ unit and $w = x+3$ unit

Therefore,the length and width of the rectangle are:

$l = x+4$ unit and $w = x+3$ unit

Answer 2

Since it is given that the formula for area is length times width and the area is already given, we are going to find out the value of the width and the length by factoring. The first thing we are going to do is to find first the factors of 12. The factor that can be used for this are 4 and 3. Then, continue with the solution.
So the correct answer for this would be the last option.  l = x + 4; w = x + 3.