Question

The work of a student to find the dimensions of a rectangle of area 8 + 16x and width 4 is shown below: Step 1: 8 + 16x Step 2: 4(4) + 4(12x) Step 3: 4(4 + 12x) Step 4: Dimensions of the rectangle are 4 and 4 + 12x In which step did the student first make an error and what is the correct step? Step 3; 4 + (4 + 12x) Step 3; 4 + (4 ⋅ 12x) Step 2; 4(2) + 4(4x) Step 2; 4(2) + 4x(2)

Answer 1

`8+16x= \\ 4(2)+4(4x)= \\ 4(2+4x)`

The student made an error in step 2. It should be 4(2)+4(4x).

Answer 2

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

Explanation:

Given the area of the rectangle = 8+16x

Width = 4

To get the length, we will use the formula for finding the area of a rectangle.

Area of a rectangle = Length × Width

Substituting the given values in the formula

Step 1:

8+16x = 4 × width

Step 2: factorising 4 from the left hand side of the equation

4(2+4x) = 4×width

4(2)+4(4x) = 4×width

Step 3:

Divide through by 4

4(2)/4+4(4x)/4 = 4×width/4

2+4x = Width

Step 4:

Dimension if the rectangle are 4 and 2+4x

Based on my step 2, it can be seen that the student made an error in the second step while bringing out the common factor.

The correct step is 4(2)+4(4x)