A rectangular piece of cloth has a length of 6 feet and a width of 1.5 feet . Brad estimates that the area is 12 square feet. His estimate is approximately what percent greater than the actual area ?

Options

A. 0.75
B. 0.66
C. 0.33
D. 0.25

Answer

To find out what percent greater Brad's estimate of the area is compared to the actual area, we can follow these steps:

### Step 1: Calculate the Actual Area
The actual area of the rectangular piece of cloth can be calculated using the formula for the area of a rectangle, which is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Given:
- Length = 6 feet
- Width = 1.5 feet

Calculating the actual area:
\[ \text{Actual Area} = 6 \, \text{feet} \times 1.5 \, \text{feet} = 9 \, \text{square feet} \]

### Step 2: Identify the Estimated Area
Brad estimates the area to be:
\[ \text{Estimated Area} = 12 \, \text{square feet} \]

### Step 3: Calculate the Difference Between Estimated and Actual Area
To find out how much greater the estimated area is than the actual area, we subtract the actual area from the estimated area:
\[ \text{Difference} = \text{Estimated Area} - \text{Actual Area} = 12 \, \text{square feet} - 9 \, \text{square feet} = 3 \, \text{square feet} \]

### Step 4: Calculate the Percent Increase
To find the percent increase, we use the formula:
\[ \text{Percent Increase} = \left( \frac{\text{Difference}}{\text{Actual Area}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percent Increase} = \left( \frac{3 \, \text{square feet}}{9 \, \text{square feet}} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 \approx 33.33\% \]

### Final Answer
Brad's estimate is approximately **33.33% greater** than the actual area.

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