A square park has area 196 square units. If its side is increased by 4 units, what will be the new area?
Answer and explanation
Correct answer: 324
The governing concept is the area formula for a square, A=s^2. Let the original side be s. Since s^2=196 and a side length is positive, s=14 units. Increasing the side by 4 gives a new side of 14+4=18 units. The new area is therefore 18^2=324 square units, so option A is correct. Option B is the square of 16 and would correspond to an incorrect increase of 2 units. Option C is the square of 20 and overestimates the new side, while option D is the square of 17 and uses an increase of only 3 units. The calculation can also be checked by expanding (14+4)^2=196+112+16=324.
Frequently asked questions
What is the correct answer to this question?
324
Why is this the correct answer?
The governing concept is the area formula for a square, A=s^2. Let the original side be s. Since s^2=196 and a side length is positive, s=14 units. Increasing the side by 4 gives a new side of 14+4=18 units. The new area is therefore 18^2=324 square units, so option A is correct. Option B is the square of 16 and would correspond to an incorrect increase of 2 units. Option C is the square of 20 and overestimates the new side, while option D is the square of 17 and uses an increase of only 3 units. The calculation can also be checked by expanding (14+4)^2=196+112+16=324.
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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