If the side of a square is increased by $8$ cm, the area increases by $192$ cm². What was the original side of the square?

Step-by-step solution

1. Step 1: Let the original side be $x$ cm.
2. Step 2: After increase, new side is $(x+8)$ cm.
3. Step 3: The increase in area is $(x+8{)}^2-x^2=192$ cm².
4. Step 4: Expand: $x^2+16x+64-x^2=192\to 16x+64=192$.
5. Step 5: Subtract 64: $16x=128$.
6. Step 6: Solve for $x$: $x=128/16=8$ cm.

Concept tested: area change due to side increase

Published 13 October 2026 · How this solution was prepared and checked