Question
The dimensions of the rectangular garden are length of 18/35 feet and width of 50/3 feet. What is the area of the garden in square feet?
425 ft2
190 ft2
384 ft2
610 ft2
425 ft2
190 ft2
384 ft2
610 ft2
Answers
GPT-4o mini
To find the area of the rectangular garden, we can use the formula:
\[
\text{Area} = \text{length} \times \text{width}
\]
Given:
- Length = \( \frac{18}{35} \) feet
- Width = \( \frac{50}{3} \) feet
Now we calculate the area:
\[
\text{Area} = \frac{18}{35} \times \frac{50}{3}
\]
We can multiply the fractions:
\[
\text{Area} = \frac{18 \times 50}{35 \times 3}
\]
Calculating the numerator:
\[
18 \times 50 = 900
\]
Calculating the denominator:
\[
35 \times 3 = 105
\]
So:
\[
\text{Area} = \frac{900}{105}
\]
Now we simplify \( \frac{900}{105} \) by finding the greatest common divisor (GCD) of 900 and 105.
First, let's simplify both numbers by dividing them by 15 (since 15 is a common factor):
\[
\frac{900 \div 15}{105 \div 15} = \frac{60}{7}
\]
Now we need to convert \( \frac{60}{7} \) into a decimal or mixed fraction:
\[
\frac{60}{7} \approx 8.5714
\]
To express it in square feet, we note that \( \frac{60}{7} = 8.5714 \) square feet is not among the options given.
Now let's evaluate:
- If we calculate the decimal \( 8.5714 \times 7 \), it equals \( 60 \), confirming that it is correct.
However, none of the available options (425 ft², 190 ft², 384 ft², 610 ft²) match this value. Please check if there are any additional details since the area derived from the calculations does not fit the outputs provided.
\[
\text{Area} = \text{length} \times \text{width}
\]
Given:
- Length = \( \frac{18}{35} \) feet
- Width = \( \frac{50}{3} \) feet
Now we calculate the area:
\[
\text{Area} = \frac{18}{35} \times \frac{50}{3}
\]
We can multiply the fractions:
\[
\text{Area} = \frac{18 \times 50}{35 \times 3}
\]
Calculating the numerator:
\[
18 \times 50 = 900
\]
Calculating the denominator:
\[
35 \times 3 = 105
\]
So:
\[
\text{Area} = \frac{900}{105}
\]
Now we simplify \( \frac{900}{105} \) by finding the greatest common divisor (GCD) of 900 and 105.
First, let's simplify both numbers by dividing them by 15 (since 15 is a common factor):
\[
\frac{900 \div 15}{105 \div 15} = \frac{60}{7}
\]
Now we need to convert \( \frac{60}{7} \) into a decimal or mixed fraction:
\[
\frac{60}{7} \approx 8.5714
\]
To express it in square feet, we note that \( \frac{60}{7} = 8.5714 \) square feet is not among the options given.
Now let's evaluate:
- If we calculate the decimal \( 8.5714 \times 7 \), it equals \( 60 \), confirming that it is correct.
However, none of the available options (425 ft², 190 ft², 384 ft², 610 ft²) match this value. Please check if there are any additional details since the area derived from the calculations does not fit the outputs provided.