Question

For a school art project, Kali has 604 square tiles measuring 1 inch on each side. She plans to use the tiles to completely cover the box in the shape of a rectangular prism below. Which statement about Kali's tiles is true?

A) Kali needs 104 more tiles to completely cover the box.

B) Kali needs 476 more tiles to completely cover the box.

C) Kali will have 260 tiles left over after completely covering the box.

D) Kali will have 534 tiles left after completely covering the box.

Answer 1

The area of the larger square is four times larger than the area of the smaller square because the side length of the larger square is twice that of the smaller one. The larger square's area is 64 square inches compared to the smaller square's 16 square inches, which abides by the rule that the ratio of the areas of similar figures is the square of the scale factor.

Step-by-step explanation:

To solve this problem, we first consider the size of the squares that Marta has. The smaller square has side lengths of 4 inches while the dimensions of the larger square are twice the size of the smaller one. Therefore, the side length of the larger square is 4 inches multiplied by 2, which equals 8 inches.

Now, let's find out how the area of the larger square compares to the area of the smaller square. The area of a square is found by squaring the length of its side. So the area of the smaller square is 4 inches × 4 inches = 16 square inches. The area of the larger square is 8 inches × 8 inches = 64 square inches.

Comparing the two areas, we see that 64 square inches is exactly 4 times 16 square inches. Therefore, the area of the larger square is 4 times larger than the area of the smaller square. This example illustrates the rule that the ratio of areas of similar figures is the square of the scale factor, which in this case is 2 squared, or 4.