11. A rectangular garden is 20 feet long, and it measures 25 feet along the diagonal. What is the area, in square feet, of the garden?
Answer: B
The area of the garden is 300 square feet.
To calculate the area of the rectangular garden, we use the formula for the area of a rectangle, which is length multiplied by width. Given that the garden is 20 feet long and the diagonal measures 25 feet, we can determine the width using the Pythagorean theorem, ultimately leading us to an area of 300 square feet.
A) 240
This option is incorrect because it does not correspond to the calculated area based on the dimensions provided. The area formula requires both length and width, and a width that would result in 240 square feet does not satisfy the diagonal measurement of 25 feet.
B) 300
This is the correct answer as it accurately represents the area of the garden, which is calculated by determining the width using the Pythagorean theorem (width = √(25² - 20²) = 15 feet), and then multiplying the length (20 feet) by the width (15 feet), resulting in an area of 300 square feet.
C) 320
This option is incorrect because an area of 320 square feet would imply an incorrect combination of length and width that does not satisfy the given diagonal measurement. The calculations based on the dimensions provided do not support this area.
D) 500
This choice is incorrect as well, as it significantly exceeds the area calculated from the known dimensions of length and width. The area of 500 square feet is not attainable with the given measurements, specifically with the diagonal constraint of 25 feet.
Conclusion
The area of 300 square feet is definitively correct as it directly results from applying the area formula to the proper dimensions derived from the garden's length and diagonal. All other options fail to align with the calculations or the geometric constraints set by the problem, confirming that B is the only valid choice.