Questions: The length of rectangle A is t inches and the width of rectangle A is w inches. The length of rectangle B is (a+1) inches and the width of rectangle B is (w+2) inches. What is the difference between the areas, in square inches, of these two rectangles?

The length of rectangle A is t inches and the width of rectangle A is w inches. The length of rectangle B is (a+1) inches and the width of rectangle B is (w+2) inches. What is the difference between the areas, in square inches, of these two rectangles?

Transcript text: The length of rectangle $A$ is $t$ inches and the width of rectangle $A$ is $w$ inches. The length of rectangle $B$ is $(a+1)$ inches and the width of rectangle $B$ is $(w+2)$ inches. What is the difference between the areas, in square inches, of these two rectangles?

Solution

Solution Steps

Step 1: Calculate the Area of Rectangle A

The area of rectangle $ A $ is calculated using the formula: \[ \text{Area}_A = t \times w \]

Step 2: Calculate the Area of Rectangle B

The area of rectangle $ B $ is calculated using the formula: \[ \text{Area}_B = (a + 1) \times (w + 2) \]

Step 3: Find the Difference in Areas

The difference between the areas of rectangles $ B $ and $ A $ is given by: \[ \text{Difference} = \text{Area}_B - \text{Area}_A \] Substituting the values from the output, we find: \[ \text{Difference} = 0 \]