A rectangle has length 15 cm and area 150 cm^2, so its width is 10 cm. Only its length is increased so that the area becomes 1 1/3 times the original (i.e., 4/3 of 150 = 200 cm^2). Find the new perimeter.

Introduction / Context:
Rectangle problems often hinge on area = length * width and perimeter = 2 * (length + width). If only one dimension changes, the other stays fixed, allowing direct computation of the new length from the new area, and then the new perimeter.

Given Data / Assumptions:

• Original length L1 = 15 cm
• Original area A1 = 150 cm^2 ⇒ width W = A1 / L1 = 150 / 15 = 10 cm
• New area A2 = (4/3) * A1 = 200 cm^2 (length only increased)

Concept / Approach:
Since width remains 10 cm, new length L2 = A2 / W. Then perimeter P2 = 2 * (L2 + W).

Step-by-Step Solution:
L2 = 200 / 10 = 20 cmP2 = 2 * (20 + 10) = 60 cm

Verification / Alternative check:
Check area: 20 * 10 = 200 cm^2, which is exactly 4/3 of 150 cm^2, confirming correctness.

Why Other Options Are Wrong:
50 cm, 70 cm, and 80 cm would imply different new lengths or widths and do not satisfy area 200 cm^2 with width fixed at 10 cm.

Common Pitfalls:
Accidentally scaling both dimensions or misreading “1 1/3 times” as “add 1/3” instead of multiply by 4/3.

Final Answer:
60 cm