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?

Rationale

The area of the garden is 300 square feet.

To find the area of a rectangular garden, we need both the length and the width. Given the length is 20 feet and we can use the diagonal to determine the width through the Pythagorean theorem, we can then calculate the area as length multiplied by width.

A (240) YOUR ANSWER

This area does not match the calculated value. If we assumed a width that would yield this area using the length of 20 feet, it would require the width to be 12 feet (since 20 x 12 = 240). However, using the Pythagorean theorem, the width is determined to be different based on the given diagonal.

B (300) CORRECT

The correct area is derived from the dimensions of the garden. Using the Pythagorean theorem, we find the width: \( w = \sqrt{25^2 - 20^2} = \sqrt{625 - 400} = \sqrt{225} = 15 \) feet. Therefore, the area is \( 20 \times 15 = 300 \) square feet.

C (320) YOUR ANSWER

This area also does not fit the dimensions provided. To achieve an area of 320 square feet with a length of 20 feet, the width would need to be 16 feet (since 20 x 16 = 320). However, calculations reveal that the actual width is 15 feet, making this option incorrect.

D (500) YOUR ANSWER

An area of 500 square feet would require a width of 25 feet (since 20 x 25 = 500). This width exceeds the diagonal measurement of 25 feet when paired with the given length of 20 feet, making this option impossible and thus incorrect.

Conclusion

The area of the rectangular garden can be accurately calculated using the dimensions provided and the Pythagorean theorem. The length of 20 feet and the calculated width of 15 feet lead to an area of 300 square feet, which is the only choice that corresponds with the given measurements. All other options are inconsistent with the dimensions of the garden.

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?

The area of the garden is 300 square feet.

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