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(2) 4x2)

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

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

Explanation:

By definition, the area of a rectangle is given by:

Area = Length × Width

In this case, we know that:

Area = 8 + 12x

Width = 4

Therefore:

Step 1: 8 + 12x

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

Step 3: 4(2 + 3x)

Therefore, the dimensions of the rectangle are 4 and 2 + 3x.

The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be 4(2) + 4(3x). Which is the second option.