A square tile has area 64 square cm. What is its side?
Answer and explanation
Correct answer: 8 cm
Let the side of the square be x centimetres. The governing formula is area of a square = side × side = x². The given area is 64 square centimetres, so x² = 64. Taking square roots gives x = ±8, but a geometrical length must be positive; therefore x = 8 cm. Substitution verifies the result because 8 × 8 = 64 square centimetres. Hence option C is correct. The values 6, 7 and 9 are not suitable because their squares are 36, 49 and 81 respectively, not 64. The negative square-root value is an algebraic possibility but cannot represent the side of a tile.
Frequently asked questions
What is the correct answer to this question?
8 cm
Why is this the correct answer?
Let the side of the square be x centimetres. The governing formula is area of a square = side × side = x². The given area is 64 square centimetres, so x² = 64. Taking square roots gives x = ±8, but a geometrical length must be positive; therefore x = 8 cm. Substitution verifies the result because 8 × 8 = 64 square centimetres. Hence option C is correct. The values 6, 7 and 9 are not suitable because their squares are 36, 49 and 81 respectively, not 64. The negative square-root value is an algebraic possibility but cannot represent the side of a tile.
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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