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Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.?
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Length of a rectangular floor is 3 m longer than its width. The area o...
Formulating the quadratic equation
Given:
- Let the width of the floor be x meters.
- The length of the floor is 3 meters longer than its width, so the length = x + 3 meters.
- The area of the floor is 54 m².
The formula for the area of a rectangle is: Area = Width x Length.
Therefore, we can write the equation as:
x(x + 3) = 54
x² + 3x = 54
x² + 3x - 54 = 0
Solving the quadratic equation
Using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 3, and c = -54.
Plugging in the values:
x = [-3 ± √(3² - 4*1*(-54))] / 2*1
x = [-3 ± √(9 + 216)] / 2
x = [-3 ± √225] / 2
x = (-3 ± 15) / 2
Therefore, the two possible values for x are:
x₁ = (-3 + 15) / 2 = 12 / 2 = 6
x₂ = (-3 - 15) / 2 = -18 / 2 = -9
Since the width cannot be negative, the width of the floor is 6 meters. The length would be x + 3 = 6 + 3 = 9 meters.
Given:
- Let the width of the floor be x meters.
- The length of the floor is 3 meters longer than its width, so the length = x + 3 meters.
- The area of the floor is 54 m².
The formula for the area of a rectangle is: Area = Width x Length.
Therefore, we can write the equation as:
x(x + 3) = 54
x² + 3x = 54
x² + 3x - 54 = 0
Solving the quadratic equation
Using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 3, and c = -54.
Plugging in the values:
x = [-3 ± √(3² - 4*1*(-54))] / 2*1
x = [-3 ± √(9 + 216)] / 2
x = [-3 ± √225] / 2
x = (-3 ± 15) / 2
Therefore, the two possible values for x are:
x₁ = (-3 + 15) / 2 = 12 / 2 = 6
x₂ = (-3 - 15) / 2 = -18 / 2 = -9
Since the width cannot be negative, the width of the floor is 6 meters. The length would be x + 3 = 6 + 3 = 9 meters.
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Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.?
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Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.?.
Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.?.
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Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.?, a detailed solution for Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? has been provided alongside types of Length of a rectangular floor is 3 m longer than its width. The area of the floor is 54 m². Formulate a quadratic equation which represents the situation and solve it using the quadratic formula. Hint: the formula for area of rectangle is (width)(length)=Area. Let x be the value of the width.? theory, EduRev gives you an
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