A rectangular photo has length 7 cm more than its breadth. After adding a 1 cm wide frame around it, the total area becomes 180 cm². What is the breadth of the photo?
Answer and explanation
Correct answer: 9 cm
The governing concept is forming a quadratic equation from the area of a rectangle. Let the photo’s breadth be x cm; its length is then x + 7 cm. Since the frame is 1 cm wide on every side, each outer dimension increases by 2 cm. Thus the outer breadth is x + 2 and the outer length is x + 9. Therefore, (x + 2)(x + 9) = 180, giving x² + 11x + 18 = 180, or x² + 11x − 162 = 0. Factoring gives (x − 9)(x + 18) = 0. The negative root x = −18 is impossible for a length, so x = 9 cm. Hence option B is correct; the other options do not satisfy the outer-area equation.
Frequently asked questions
What is the correct answer to this question?
9 cm
Why is this the correct answer?
The governing concept is forming a quadratic equation from the area of a rectangle. Let the photo’s breadth be x cm; its length is then x + 7 cm. Since the frame is 1 cm wide on every side, each outer dimension increases by 2 cm. Thus the outer breadth is x + 2 and the outer length is x + 9. Therefore, (x + 2)(x + 9) = 180, giving x² + 11x + 18 = 180, or x² + 11x − 162 = 0. Factoring gives (x − 9)(x + 18) = 0. The negative root x = −18 is impossible for a length, so x = 9 cm. Hence option B is correct; the other options do not satisfy the outer-area equation.
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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