Question

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

• A. \(45\) cm
• B. \(50\) cm
• C. \(55\) cm
• D. \(53\) cm
• E. \(48\) cm

Answer 1

The Correct Option is B

Concept: Area remains same:

• Original rectangle area = New square area

Step 1: Assume dimensions.
Let length \(= l\), width \(= b\) \[ \text{Area} = lb \]
Step 2: Form square condition.
After change: \[ l - 4 = b + 3 \Rightarrow l = b + 7 \]
Step 3: Use area equality.
\[ lb = (l - 4)(b + 3) \] Substitute \(l = b + 7\): \[ (b+7)b = (b+3)^2 \]
Step 4: Solve equation.
\[ b^2 + 7b = b^2 + 6b + 9 \] \[ 7b - 6b = 9 \Rightarrow b = 9 \] \[ l = b + 7 = 16 \]
Step 5: Find perimeter.
\[ \text{Perimeter} = 2(l + b) = 2(16 + 9) = 50 \]
Step 6: Option analysis.

• (A) 45: Incorrect $\times$
• (B) 50: Correct \checkmark
• (C) 55: Incorrect $\times$
• (D) 53: Incorrect $\times$
• (E) 48: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).