Question 36

The area of the rectangle is 403.68 in squared.

To find the area of the rectangle, we first need to determine its width using the Pythagorean theorem. Given the diagonal (29 in) and the length (23.2 in), we calculate the width and then use it to find the area.

A) 504.60 in squared

This option is incorrect. The area of a rectangle is calculated as length times width. Given the dimensions provided, there is no combination that results in an area of 504.60 in squared, making this option unviable.

B) 201.84 in squared

This option is also incorrect. The area of 201.84 in squared does not correspond to the rectangle's dimensions derived from the diagonal and length. The calculations for the width reveal that this area cannot be achieved.

C) 403.68 in squared

This is the correct answer. By applying the Pythagorean theorem, we find the width to be approximately 21.6 in. The area is then calculated as length (23.2 in) multiplied by width (21.6 in), resulting in an area of 403.68 in squared.

D) 372.80 in squared

This option is incorrect. The area of 372.80 in squared does not align with the calculations derived from the rectangle's dimensions. The computed width and length do not support this area as a valid outcome.

Conclusion

The area of the rectangle is definitively 403.68 in squared, as derived from the correct application of the Pythagorean theorem to find the missing width. All other options fail because they do not correspond to the rectangle's actual dimensions or calculated area. Thus, C is the only viable choice.