Question

In the diagram below, the dimensions of a student ID card are shown rounded to the nearest whole inch. 4 in. ili 3 in. Which of the following could be the actual area, in square inches, of the front of the card?Options A. 8B. 8.5C. 15.5D. 16

Answer 1

We have a card that is has dimensions that are rounded to the nearest inch. One side is 4 in. and the other is 3 in.

As these values correspond to rounded values, we know that the 4-in side can have a length between 3.5 inches and 4.5 inches.

This is because if the length was lower than 3.5 inches, the rounded value would be 3 inches and not 4 inches. Similarly, if the length was greater than 4.5 inches, the rounded value would have been 5 inches and not 4 inches.

For the 3-in side, it can have a length between 2.5 in and 3.5 in.

Then, the area can be any value between the product of the minimum measures and the product of the maximum measures.

Then, the minimum area is:

`A_(\min )=3.5\cdot2.5=8.75`

And the maximum area is:

`A_(\max )=4.5\cdot3.5=15.75`

The area of the ID card can be any value between 8.75 sq in and 15.75 sq in.

From the options, the only value that is within the interval is Option C: 15.5.