Question

What mistake, if any, did Lara make in her figure for completing the square of the expression x^2 + 7x?

a. Lara should have added rectangles with areas of 5x square units and 2x square units instead of 4x square units and 3x square units.
b. Lara should have added rectangles with areas of 3.5x square units and 3.5x square units instead of 4x square units and 3x square units.
c. Lara did not make a mistake.
d. Lara should have added rectangles with areas of 16 square units and 9 square units instead of 4x square units and 3x square units.

Answer 1

The area of the larger square is four times larger than the area of the smaller square because the area of similar figures is proportional to the square of their corresponding side lengths.

Step-by-step explanation:

The area of a square is calculated by squaring the length of one of its sides. If Marta has one square with side length of 4 inches and another square with dimensions that are twice as large (meaning each side is 8 inches because 2 x 4 inches = 8 inches), the area of the larger square can be found by squaring the side length, resulting in 8 inches x 8 inches = 64 square inches. To compare this to the smaller square, we calculate the area of the smaller square by squaring its side length as well: 4 inches x 4 inches = 16 square inches. Since 64 square inches is four times 16 square inches, the area of the larger square is four times larger than the area of the smaller square.