Question

for what values of n is the perimeter of square a less than the perimeter of rectangle b?

n a 3 b (with length n+2)

a. n < 5
b. n ≤ 6
c. n ≤ 5
d. n < 6

Explanation:

Step1: Calculate perimeter of square A

Perimeter of square A = $4n$

Step2: Calculate perimeter of rectangle B

Perimeter of rectangle B = $2[(n+2)+3] = 2(n+5) = 2n + 10$

Step3: Set up inequality

$4n < 2n + 10$

Step4: Solve for n

$4n - 2n < 10$ → $2n < 10$ → $n < 5$? Wait, correction: Wait rectangle B's perimeter is 2(length + width) = 2(n+2 +3)=2(n+5)=2n+10. Square perimeter is 4n. So 4n < 2n+10 → 2n <10 → n<5? But wait option D is n<6. Wait wait, did I miscalculate? Wait no, wait let's recheck: Square A perimeter: 4side =4n. Rectangle B: length n+2, width 3, perimeter=2(n+2 +3)=2(n+5)=2n+10. So 4n <2n+10 → 2n<10 →n<5. But option A is n<5. Wait but why option D? Wait maybe I misread the figure? Wait no, the user's figure: square A has side n, rectangle B has length n+2 and width 3. So 4n <2(n+2+3) →4n<2n+10→2n<10→n<5. So option A is correct? Wait but let's check again: If n=5: square perimeter=20, rectangle perimeter=2(5+2+3)=210=20, so equal. So n<5 is when square perimeter is less. So option A is n<5, which is correct. Wait but maybe the user's figure has different dimensions? Wait no, the user wrote: square A side n, rectangle B length n+2, width3. So yes, 4n <2(n+5)→n<5. So answer is A. n<5.</think_never_used_51bce0c785ca2f68081bfa7d91973934># Answer:
A. n < 5

Step1: Compute perimeter of square A

Perimeter of square A = $4n$

Step2: Compute perimeter of rectangle B

Perimeter of rectangle B = $2[(n+2)+3] = 2n + 10$

Step3: Set up inequality

$4n < 2n + 10$

Step4: Solve for n

$2n < 10 \implies n < 5$

Answer:

D. n < 6