Rectangle from perimeter and side difference; triangle on its diagonal:\nA rectangle has perimeter 84 m and its length is 6 m more than its breadth. Find the area of a triangle whose base equals the rectangle’s diagonal and height equals the rectangle’s length.

Introduction / Context:
First recover the rectangle’s dimensions, compute its diagonal, then evaluate the triangle area using base = diagonal and height = length.

Given Data / Assumptions:

• Perimeter P = 84 ⇒ L + B = 42.
• L = B + 6.
• Triangle base = diagonal; height = L.

Concept / Approach:
Solve for L and B, compute diagonal d = √(L^2 + B^2), then triangle area A = (1/2)*d*L.

Step-by-Step Solution:

Verification / Alternative check:
Dimensions satisfy perimeter 2(24 + 18) = 84.

Why Other Options Are Wrong:
380, 400 do not match the computed area; “360 metre” has wrong units for area.

Common Pitfalls:
Using 2(L+B) wrongly or forgetting to halve for triangle area.

Final Answer:
360 sq metre.