Rectangle from perimeter and side difference; triangle on its diagonal: A 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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: 1) (B + 6) + B = 42 ⇒ 2B = 36 ⇒ B = 18; L = 24.2) d = √(24^2 + 18^2) = √(576 + 324) = √900 = 30 m.3) Triangle area = 0.5 * 30 * 24 = 360 sq m. 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.

Rectangle from perimeter and side difference; triangle on its diagonal: A 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.

More Questions from Area

Discussion & Comments