Question

If a sufficiently large square is changed into a rectangle by making it 7 cm less wide and 7 cm taller, how much does the area change?

a) 7 cm^2
b) 14 cm^2
c) 49 cm^2
d) 98 cm^2

Answer 1

A large square transformed into a rectangle by decreasing its width by 7 cm and increasing its height by 7 cm results in a change in area of 49 cm^2.

Step-by-step explanation:

If a sufficiently large square is changed into a rectangle by making it 7 cm less wide and 7 cm taller, the change in the area can be calculated by finding the area of the square first and then the area of the resulting rectangle. Let's assume the side of the square is x cm. The area of the square is x2 cm2. After making the square 7 cm less wide and 7 cm taller, it becomes a rectangle with dimensions (x - 7) cm by (x + 7) cm. The area of the rectangle is (x - 7)(x + 7) cm2, which simplifies to x2 - 49 cm2. The change in area is the difference between the areas of the square and the rectangle, which is x2 - (x2 - 49 cm2), resulting in a change of 49 cm2. The correct answer is c) 49 cm2.