The side of a square tile is (x-13) cm, and its area is 1600 square cm. What is the value of (x)?
Answer and explanation
Correct answer: 53
The area of a square is (side)^2. Thus, (x-13)^2=1600=40^2. Since a side length must be positive, x-13=40, giving x=53. The other algebraic possibility, x-13=-40, would make the side negative and is therefore invalid. Exam tip: reject negative roots when the variable represents a length, distance, or measurement. Option 47 is incorrect because it gives a side of 34 cm, whose area is not 1600 square cm.
Frequently asked questions
What is the correct answer to this question?
53
Why is this the correct answer?
The area of a square is (side)^2. Thus, (x-13)^2=1600=40^2. Since a side length must be positive, x-13=40, giving x=53. The other algebraic possibility, x-13=-40, would make the side negative and is therefore invalid. Exam tip: reject negative roots when the variable represents a length, distance, or measurement. Option 47 is incorrect because it gives a side of 34 cm, whose area is not 1600 square cm.
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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