Question

The side lengths of a square are each 4p. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle?

Answer 1

The student asks about altering a square's dimensions to form a rectangle and finding its area. By changing the side lengths from 4p to (4p + 3) and (4p - 3), the area of the rectangle is calculated to be 16p² - 9.

Step-by-step explanation:

The student's question involves creating a rectangle from a square by altering its dimensions. Each side of the original square is 4p. Adding 3 to the length and subtracting 3 from the width results in a rectangle with a length of (4p + 3) and a width of (4p - 3). To calculate the area of the rectangle, we multiply the length by the width:

Area = Length × Width

Area = (4p + 3) × (4p - 3)

Area = 16p² - 9

This is the area of the resulting rectangle after adjusting the dimensions of the original square.