A square park has area 144. If its side is increased by 3, what will be the new area?
Answer and explanation
Correct answer: 225
For a square, area equals the square of its side. If the original side is s, then s² = 144. Because a side length is positive, s = √144 = 12. Increasing the side by 3 gives a new side of 12 + 3 = 15. The new area is therefore 15² = 225. This can also be checked by expansion: (12 + 3)² = 12² + 2(12)(3) + 3² = 144 + 72 + 9 = 225. Option B, 169, would correspond to a side of 13 and an increase of only 1; option C corresponds to a side of 14; option D is not the square of the new side. Hence option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
For a square, area equals the square of its side. If the original side is s, then s² = 144. Because a side length is positive, s = √144 = 12. Increasing the side by 3 gives a new side of 12 + 3 = 15. The new area is therefore 15² = 225. This can also be checked by expansion: (12 + 3)² = 12² + 2(12)(3) + 3² = 144 + 72 + 9 = 225. Option B, 169, would correspond to a side of 13 and an increase of only 1; option C corresponds to a side of 14; option D is not the square of the new side. Hence option A is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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