A rectangle has area 154 cm2. Its length is 4 times the breadth plus 4 cm.…

For any rectangle, Area = Length × Breadth. When a word problem expresses one dimension in terms of the other using a variable and gives the area, substituting the algebraic expressions into this formula and simplifying produces the required equation in standard form (ax² + bx + c = 0).

1. Let the breadth = b cm. Since the length is 4 times the breadth plus 4 cm, length = (4b + 4) cm.

2. Area = Length × Breadth = (4b + 4) × b.

3. Expanding the product: (4b + 4) × b = 4b2+ 4b.

4. The area is given as 154 cm2, so 4b2+ 4b = 154.

5. Moving all terms to one side gives the quadratic equation: 4b2+ 4b − 154 = 0.

Reversing the last step confirms the setup: 4b2+ 4b − 154 = 0 is equivalent to 4b2+ 4b = 154, which is exactly Area = (4b + 4) × b = 154 as given — no extra constant was introduced, so 154 (the area itself) is the correct constant term, not a fragment of the length expression or a mistyped digit.