Question

The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below: Step 1: 8 + 12x Step 2: 4(4) + 4(8x) Step 3: 4(4 + 8x) Step 4: Dimensions of the rectangle are 4 and 4 + 8x In which step did the student first make an error and what is the correct step? Step 2; 4(2) + 4x(2) Step 2; 4(2) + 4(3x) Step 3; 4 + (4 + 8x) Step 3; 4 + (4 ⋅ 8x)

Answer 1

The student ought to be factoring 4 from the terms in the area expression. The appropriate choice is ...

... Step 2; 4(2) + 4(3x)

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that the area of a rectangle is 8+12x and width of the rectangle is 4.

We need to find the dimensions of the rectangle.

Area of a rectangle is

$A=length\times width$

It means the factors of expression of area represent the dimensions.

The correct steps are shown below:

Step 1: 8 + 12x

Step 2: 4(2) + 4(3x)

Step 3: 4(2 + 3x)

Step 4: Dimensions of the rectangle are 4 and 2 + 3x.

Student made an error in step 2 and the correct step is 4(2) + 4(3x). Therefore the correct option is 2.