Question

The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet. Cameron determines the area of the wall to be 1423.125 square feet. Which best explains the reasonableness of Cameron’s solution?

Cameron’s solution is reasonable because there are four decimal places in the factors and four decimal places in the product.
Cameron’s solution is reasonable because there are three decimal places in the factors and three decimal places in the product.
Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.
Cameron’s solution is unreasonable because 10 times 10 is 100, and 100 is not close to his product

Answer 1

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.

Explanation:

Area of a rectangle:

The area of a rectangle, of length l and height h, is given by:

`A = lh`

The length of a rectangular wall is 16.5 feet. The height of the wall is 8.625 feet.

This means that
`l = 16.5, h = 8.625`

Estimate of the area:

To use an "easy" multiplication, lets consider
`l = 17, h = 9`. So

`A = lh = 17(9) = 153`

Cameron determines the area of the wall to be 1423.125 square feet.

Very far from the area of 153, which means that he made a confusion with the decimal places. Thus, the correct answer is:

Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product.