Rectangle — Length 30 cm, area 720 sq cm. Increasing only length makes area 1.25 times the original. Find the new perimeter.

Introduction / Context:
When one side changes and the other remains fixed, area changes proportionally to the changing side. Use the target area to find the new length, then compute the new perimeter.

Given Data / Assumptions:

• Original L = 30 cm
• Original A = 720 sq cm ⇒ B = 720 / 30 = 24 cm
• New area A' = 1.25 * 720 = 900 sq cm
• Only length changes

Concept / Approach:
New length L' = A' / B. Then perimeter P' = 2(L' + B).

Step-by-Step Solution:
B = 24 cmL' = 900 / 24 = 37.5 cmP' = 2(37.5 + 24) = 2 * 61.5 = 123 cm

Verification / Alternative check:
Area check: 37.5 * 24 = 900 sq cm, which is 1.25 × 720.

Why Other Options Are Wrong:
Other perimeters correspond to incorrect divisions or rounding errors.

Common Pitfalls:
Changing both sides or misreading 1 1/4 as 1.4 instead of 1.25.

Final Answer:
123 cm