The diagonal of a rectangle measures 29 in, and the length of the rectangle is 23.2 in. What is the area of this rectangle?

Rationale

The area of the rectangle is 403.68 in squared.

To find the area of a rectangle, we multiply its length by its width. Given the diagonal and one side, we can use the Pythagorean theorem to calculate the missing side (width) and then determine the area.

A (504.60 in squared) YOUR ANSWER

This area is too large given the rectangle's dimensions. Using the length of 23.2 in and the calculated width, the area cannot exceed 403.68 in squared as derived from the correct dimensions.

B (201.84 in squared) YOUR ANSWER

This area is significantly smaller than what we expect for a rectangle with a diagonal of 29 in and a length of 23.2 in. The calculation of the width leads to a larger area than this option suggests.

C (403.68 in squared) CORRECT

This is the correct calculation of the rectangle's area. First, we determine the width using the Pythagorean theorem: \( \text{width} = \sqrt{29^2 - 23.2^2} \approx 19.2 \) in. The area is then calculated as \( 23.2 \times 19.2 = 403.68 \) in squared.

D (372.80 in squared) YOUR ANSWER

This area is also incorrect as it underestimates the calculated area. Given the dimensions, the area derived from the length and width should be 403.68 in squared, indicating that the width must be greater than the value that would yield this area.

Conclusion

In calculating the area of a rectangle, it is essential to derive both the length and width accurately; thus, knowing the diagonal assists in this process. For the given rectangle, the length of 23.2 in and the calculated width resulted in an area of 403.68 in squared. The other choices either miscalculate or misinterpret the geometric relationship between the rectangle's dimensions.

The diagonal of a rectangle measures 29 in, and the length of the rectangle is 23.2 in. What is the area of this rectangle?

The area of the rectangle is 403.68 in squared.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test