Perimeter from speed and time — rectangular park area: Radhika runs along the boundary of a rectangular park at 12 km/h and completes one full round in 15 minutes. If the park’s length is four times its breadth, find the area of the park in square meters.

Introduction / Context:Speed and time give distance, which here equals the perimeter of a rectangle. With a length-to-breadth ratio, we can back out the sides and area.

Given Data / Assumptions:

• Speed = 12 km/h
• Time = 15 minutes = 0.25 h → distance (perimeter) = 12 * 0.25 = 3 km = 3000 m
• Length = 4 * breadth

Concept / Approach:Perimeter P = 2(L + B). With L = 4B → P = 2(5B) = 10B. Solve B from P, then find L and area A = L * B.

Step-by-Step Solution:10B = 3000 → B = 300 mL = 4B = 1200 mArea A = 1200 * 300 = 360000 m2

Verification / Alternative check:Perimeter check: 2(1200 + 300) = 3000 m, which matches the lap distance.

Why Other Options Are Wrong:360002 is dimensionally incorrect; 3600 m2 mis-scales by a factor of 100.

Common Pitfalls:Converting 15 minutes incorrectly or mixing km and meters.

Final Answer:360000 m2