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Class 10 Mathematics Quadratic Equations Word Problems and ApplicationsHardLevel 41

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A square field has a side length of (x) metres. If the side is increased by 8 metres, the area increases by 1216 square metres. What is the value of (x)?

Answer and explanation

Correct answer: 72

The increase in area is ((x+8)^2-x^2=1216). Expanding gives (16x+64=1216), so (16x=1152) and (x=72) metres. Therefore, option B is correct. Exam tip: For a change in the side of a square, use ((x+a)^2-x^2=2ax+a^2); do not incorrectly set ((x+a)^2=1216).

Related tags

Quadratic Equations Square Area Word Problems

Frequently asked questions

What is the correct answer to this question?

72

Why is this the correct answer?

The increase in area is ((x+8)^2-x^2=1216). Expanding gives (16x+64=1216), so (16x=1152) and (x=72) metres. Therefore, option B is correct. Exam tip: For a change in the side of a square, use ((x+a)^2-x^2=2ax+a^2); do not incorrectly set ((x+a)^2=1216).

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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