Question

For this model showing a unit square divided into smaller square tiles, the shaded tiles form a rectangle. Use fractions to complete the sentences. The side length of each small tile is ___ units. The area of each small tile is ___ square units. The area of the shaded rectangle is ___ square units.

a) 1/2, 1/2, 1/4

b) 1/4, 1/4, 1/8

c) 1/3, 1/3, 1/9

d) 1/5, 1/5, 1/25

Answer 1

The area of a larger square with side lengths twice that of a smaller one is four times greater, as the area is calculated by squaring the side lengths and comparing the resulting areas.

Step-by-step explanation:

When comparing the area of a larger square to a smaller one where the side lengths of the larger square are twice that of the smaller square, the area increases by a scale factor squared. If the side length of the smaller square is 4 inches, then the side length of the larger square will be 8 inches (4 inches x 2).

Since the area of a square is calculated by squaring the side length, we take the side length of the smaller square (4 inches) and calculate its area (4 inches x 4 inches = 16 square inches). For the larger square, we square its side length as well (8 inches x 8 inches = 64 square inches).

Comparing the two areas, the area of the larger square is 4 times greater than that of the smaller square, because (8 x 8) / (4 x 4) equals 64/16, which simplifies to 4.