Question

The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 4 cm, the area of the rectangle increases by 52 cm2. The length of the rectangle (in cm) is:

• A. 36
• B. 32
• C. 38
• D. 34

Answer 1

Answer:

D. 34

Solution: Given : Length of rectangle is twice it's breadth. Length decreases by 4 cm and breadth increases by 4 cm. Area of rectangle increases by 52 cm2. Formula used : Area of rectangle = Length × Breadth Calculation : According to question, ⇒ L = 2B ⇒ L/B = 2x/1x Area of rectangle = 2x2 Now, ⇒ (2x - 4) × (x + 4) = 2x2 + 52 ⇒ 2x2 + 8x - 4x -16 = 2x2 + 52 ⇒ 4x = 68 ⇒ x = 17 Length of rectangle = 2x = 2 × 17 = 34 cm ∴ The correct answer is 34 cm.