A (3\text{ cm}) wide strip is cut from one side of a square sheet. The remaining rectangle has area (70\text{ cm}^2). What was the side of the original square?
Answer and explanation
Correct answer: (10\text{ cm})
Let the side of the original square be x centimetres. Cutting away a strip 3 centimetres wide from one side leaves a rectangle whose dimensions are x and x-3. Its area is therefore x(x-3), and the given information produces x(x-3)=70. Since a side length must be positive and greater than 3, only a physically meaningful positive solution can be used.
Expanding gives x^2-3x-70=0. Factoring yields (x-10)(x+7)=0, so x=10 or x=-7. A length cannot be negative, so x=-7 is rejected. With x=10, the remaining rectangle has dimensions 10 cm and 7 cm, and its area is 70 square centimetres. Therefore the original square side was 10 cm, option B.
Frequently asked questions
What is the correct answer to this question?
(10\text{ cm})
Why is this the correct answer?
Let the side of the original square be x centimetres. Cutting away a strip 3 centimetres wide from one side leaves a rectangle whose dimensions are x and x-3. Its area is therefore x(x-3), and the given information produces x(x-3)=70. Since a side length must be positive and greater than 3, only a physically meaningful positive solution can be used.
Expanding gives x^2-3x-70=0. Factoring yields (x-10)(x+7)=0, so x=10 or x=-7. A length cannot be negative, so x=-7 is rejected. With x=10, the remaining rectangle has dimensions 10 cm and 7 cm, and its area is 70 square centimetres. Therefore the original square side was 10 cm, option B.
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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