Rectangle — Area is 75 sq units and length is 5 more than twice the width. Find the perimeter.

Introduction / Context:This is a quadratic relation between width and length because area = L * W and L is a linear function of W. Solve for W, then compute L and the perimeter 2(L + W).

Given Data / Assumptions:

• A = 75
• L = 2W + 5

Concept / Approach:Set (2W + 5) * W = 75, solve the quadratic for a positive width, then compute L and the perimeter.

Step-by-Step Solution:2W^2 + 5W − 75 = 0Discriminant = 25 + 600 = 625 ⇒ W = (−5 + 25)/4 = 5L = 2*5 + 5 = 15Perimeter = 2(L + W) = 2(15 + 5) = 40 unit

Verification / Alternative check:A = 15 * 5 = 75 ✔

Why Other Options Are Wrong:30, 24, and 20 units are typical misreads; 50 unit overestimates.

Common Pitfalls:Choosing the negative quadratic root or forgetting perimeter is twice the sum.

Final Answer:40 unit