Answer:
[tex]\sf 5a + 22[/tex] unit²
Step-by-step explanation:
To find the difference in the areas of rectangle A and rectangle B, we first need to calculate the areas of both rectangles.
The area [tex]\sf A[/tex] of a rectangle is given by the formula:
[tex]\sf A = \textsf{length} \times \textsf{width} [/tex]
For rectangle A:
- Length: [tex]\sf 2a + 7[/tex]
- Width: [tex]\sf 4[/tex]
So, the area of rectangle A is:
[tex]\sf A_A = (2a + 7) \times 4 [/tex]
For rectangle B:
- Length: [tex]\sf a + 2[/tex]
- Width: [tex]\sf 3[/tex]
So, the area of rectangle B is:
[tex]\sf A_B = (a + 2) \times 3 [/tex]
Now, we can find the difference in the areas:
[tex]\begin{aligned} \textsf{Difference} & \sf = A_A - A_B \\\\ & \sf = (2a + 7) \times 4 - (a + 2) \times 3 \\\\ & \sf = 8a + 28 - 3a - 6 \\\\ & \sf = 5a + 22 \end{aligned}[/tex]
So, the areas of rectangle A and rectangle B are larger by [tex]\sf 5a + 22[/tex] unit².
